Class 7 ICSE Mathematics: Linear Equations and Inequations
1. Introduction
Linear equations and inequations are fundamental topics in algebra. They help us understand how quantities relate to each other using simple algebraic expressions. Mastering these concepts builds a strong foundation for higher mathematics.
- Linear Equation: An equation in which the variable has a power of 1.
Example: ( 2x + 5 = 11 ) - Linear Inequation: An inequality involving a variable to the first power.
Example: ( 3x – 4 > 5 )
2. Linear Equations in One Variable
2.1 Definition
A linear equation in one variable is an equation of the form:
[
ax + b = 0
]
Where (a) and (b) are constants, (a \neq 0), and (x) is the variable.
2.2 Solving Linear Equations
Step 1: Simplify both sides of the equation (remove brackets, combine like terms).
Step 2: Move variable terms to one side and constants to the other.
Step 3: Divide or multiply to isolate the variable.
Example 1: Solve ( 3x + 7 = 16 )
Solution:
[
3x + 7 = 16
]
[
3x = 16 – 7
]
[
3x = 9
]
[
x = \frac{9}{3} = 3
]
Example 2: Solve ( 5 – 2x = 9 )
Solution:
[
5 – 2x = 9
]
[
-2x = 9 – 5
]
[
-2x = 4
]
[
x = \frac{4}{-2} = -2
]
3. Linear Equations in Two Variables
3.1 Definition
A linear equation in two variables is of the form:
[
ax + by + c = 0
]
Where (a), (b), and (c) are constants, (x) and (y) are variables, and at least one of (a) or (b) is not zero.
3.2 Solving by Substitution
- Solve one equation for one variable in terms of the other.
- Substitute into the second equation.
- Solve for the remaining variable.
Example: Solve
[
x + y = 7
]
[
2x – y = 4
]
Solution:
From the first equation: ( y = 7 – x )
Substitute into the second:
[
2x – (7 – x) = 4
]
[
2x – 7 + x = 4
]
[
3x – 7 = 4
]
[
3x = 11
]
[
x = \frac{11}{3}
]
Then:
[
y = 7 – \frac{11}{3} = \frac{21 – 11}{3} = \frac{10}{3}
]
4. Linear Inequations in One Variable
4.1 Definition
A linear inequation in one variable is an inequality involving a variable to the first power:
[
ax + b > 0, \quad ax + b \ge 0, \quad ax + b < 0, \quad ax + b \le 0
]
4.2 Solving Steps
- Simplify both sides.
- Move constants to one side.
- Divide or multiply by the coefficient of the variable (reverse the inequality if multiplying/dividing by a negative number).
Example 1: Solve ( 2x – 5 > 1 )
Solution:
[
2x – 5 > 1
]
[
2x > 6
]
[
x > 3
]
Example 2: Solve ( -3x + 4 \le 10 )
Solution:
[
-3x + 4 \le 10
]
[
-3x \le 6
]
Divide by -3 (reverse inequality):
[
x \ge -2
]
5. Graphical Representation
- Linear Equations in Two Variables: Represent a straight line on a graph.
- Linear Inequations: Represent a region on one side of the line.
Steps to Graph:
- Write the equation in (y = mx + c) form.
- Plot at least 2 points and draw the line.
- For inequalities, shade the region satisfying the inequality.
6. Key Tips for ICSE Students
- Always simplify the equation first.
- Check your solution by substituting back into the original equation.
- Remember: Multiply/divide by a negative? Reverse the inequality.
- For two-variable equations, practice substitution and elimination methods.
- Graphical understanding helps in visualizing solutions for inequalities.
7. Practice Questions
Linear Equations:
- Solve ( 4x + 7 = 19 )
- Solve ( 3x – 5 = 16 )
- Solve:
[
x + y = 10, \quad 2x – y = 3
]
Linear Inequations:
- Solve ( 5x – 8 > 12 )
- Solve ( -2x + 7 \le 3 )
Graphical:
- Graph ( y = 2x + 1 )
- Shade the region for ( y \ge 2x – 3 )
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Below are EASY, FULL, EXAM-ORIENTED NOTES on
Linear Equations – Class 7 (ICSE / ICSE Plus)
(Simple language • Step-by-step • Beginner friendly • Exam ready)
These notes are written from zero level and are suitable for average students, revision, and full marks preparation.
CHAPTER: LINEAR EQUATIONS
- INTRODUCTION
In earlier classes, you have solved simple number problems like:
5 + _ = 12 _ − 7 = 10
Such problems contain unknown values.
In Class 7, these unknown values are represented by letters like x, y, a, b.
When a mathematical statement contains an equal sign (=) and a variable, it is called an equation. - WHAT IS A VARIABLE?
A variable is a symbol (usually a letter) that represents an unknown number.
Examples:
x + 5 = 12
3y = 15
a − 7 = 10
Here x, y, a are variables. - WHAT IS AN EQUATION?
An equation is a mathematical statement that shows equality between two expressions using the sign =.
Examples:
7 + 5 = 12 ✔
x + 3 = 10 ✔
4y − 2 = 14 ✔ - WHAT IS A LINEAR EQUATION?
A linear equation is an equation in which:
The highest power of the variable is 1
It has only one variable (in Class 7)
General form:
a, b, c are numbers
x is the variable - EXAMPLES OF LINEAR EQUATIONS
✔ x + 7 = 12
✔ 3x = 15
✔ 5x − 4 = 16
✔ x/2 = 6 - NON-EXAMPLES (NOT LINEAR EQUATIONS)
❌ x² + 3 = 7 (power is 2)
❌ xy = 6 (two variables)
❌ 1/x = 5 - TERMS USED IN LINEAR EQUATIONS
(a) Variable
The unknown value → x, y, a, etc.
(b) Constant
A fixed number → 3, 7, 10, −5
(c) Coefficient
The number multiplied with the variable.
Example:
In 5x, coefficient of x = 5 - SOLUTION OF A LINEAR EQUATION
The solution of a linear equation is the value of the variable that makes the equation true.
Example:
x + 5 = 9
If x = 4, then
4 + 5 = 9 ✔ (True)
So, x = 4 is the solution - BASIC RULES FOR SOLVING LINEAR EQUATIONS
🔹 Rule 1: Do the same operation on both sides
🔹 Rule 2: Change side → change sign
From LHS to RHS
Sign changes
- becomes
−
− becomes
+
× becomes
÷
÷ becomes
×
- METHOD OF SOLVING LINEAR EQUATIONS
Step-by-step method:
Write the equation
Bring variables on one side
Bring constants on the other side
Simplify
Find the value of the variable - TYPE 1: SIMPLE LINEAR EQUATIONS
Example 1:
x + 7 = 15
Solution:
x = 15 − 7
x = 8
Example 2:
x − 9 = 6
Solution:
x = 6 + 9
x = 15 - TYPE 2: LINEAR EQUATIONS WITH MULTIPLICATION
Example:
3x = 18
Solution:
x = 18 ÷ 3
x = 6
Example:
5x = 25
x = 25 ÷ 5
x = 5 - TYPE 3: LINEAR EQUATIONS WITH DIVISION
Example:
x/4 = 7
Solution:
x = 7 × 4
x = 28
Example:
x/6 = 5
x = 5 × 6
x = 30 - TYPE 4: TWO-STEP LINEAR EQUATIONS
Example:
3x + 4 = 19
Solution:
3x = 19 − 4
3x = 15
x = 15 ÷ 3
x = 5
Example:
5x − 7 = 18
5x = 18 + 7
5x = 25
x = 5 - LINEAR EQUATIONS WITH FRACTIONS
Example:
x/2 + 3 = 7
Solution:
x/2 = 7 − 3
x/2 = 4
x = 8
Example:
x/5 − 2 = 6
x/5 = 8
x = 40 - WORD PROBLEMS ON LINEAR EQUATIONS
Example 1:
The sum of a number and 7 is 20. Find the number.
Let the number be x
x + 7 = 20
x = 13
Example 2:
Five times a number is 45. Find the number.
5x = 45
x = 9 - AGE PROBLEMS
Example:
Riya is 5 years older than her brother.
Brother’s age = x
Riya’s age = x + 5
If Riya is 17 years old, find brother’s age.
x + 5 = 17
x = 12 - MONEY PROBLEMS
Example:
A pen costs ₹15 more than a pencil.
If pen costs ₹45, find the price of the pencil.
Let pencil cost = x
x + 15 = 45
x = 30 - CHECKING THE SOLUTION
Always substitute the value back into the equation.
Example:
x + 6 = 14
x = 8
Check:
8 + 6 = 14 ✔ - COMMON MISTAKES TO AVOID
❌ Forgetting sign change
❌ Dividing only one side
❌ Calculation mistakes
❌ Not checking the answer - IMPORTANT EXAM TIPS
✔ Write steps clearly
✔ Use proper signs
✔ Final answer must be written clearly
✔ Do rough work carefully - VERY SHORT QUESTIONS (1 MARK)
What is a variable?
Write one linear equation.
What is the degree of a linear equation? - SHORT QUESTIONS (2 MARKS)
Solve: x + 9 = 20
Solve: 4x = 28 - LONG QUESTIONS (4 MARKS)
Solve: 3x − 5 = 16
The sum of a number and 12 is 30. Find the number. - ONE-PAGE QUICK REVISION
Variable → unknown value
Linear equation → highest power 1
Solve → isolate the variable
Same operation on both sides
Check solution
✅ CONCLUSION
Linear equations form the foundation of algebra.
Understanding this chapter well will help in higher classes like 8, 9, and 10.
🎯 This chapter is COMPLETE for Class 7 (ICSE / ICSE Plus)
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📝 Worksheets with answers
📘 Word problems only
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This part focuses on advanced clarity, more examples, practice types, HOTS, and exam writing style.
LINEAR EQUATIONS – EXTENDED NOTES (PART 2)
(Class 7 ICSE / ICSE Plus)
- BALANCE METHOD (IMPORTANT CONCEPT)
A linear equation is like a balance scale.
Whatever you do on one side, you must do the same on the other side to keep it balanced.
Example:
x + 4 = 10
If we remove 4 from the left side, we must remove 4 from the right side.
x + 4 − 4 = 10 − 4
x = 6 - TRANSPOSITION METHOD (MOST USED IN EXAMS)
Transposition means moving a term from one side of the equation to the other by changing its sign.
Rules of Transposition:
Original Sign
After Transposition
+
−
−
+
×
÷
÷
×
Example:
x + 9 = 17
Move +9 to RHS → becomes −9
x = 17 − 9
x = 8
Example:
7x = 56
Move 7 to RHS → becomes ÷7
x = 56 ÷ 7
x = 8 - LINEAR EQUATIONS WITH NEGATIVE NUMBERS
Example 1:
x − 5 = −2
x = −2 + 5
x = 3
Example 2:
−3x = 12
x = 12 ÷ (−3)
x = −4
Example 3:
x + (−7) = 10
x = 10 + 7
x = 17 - EQUATIONS WITH VARIABLES ON BOTH SIDES
In such equations, the variable appears on both sides.
Example:
2x + 5 = x + 11
Step 1: Bring variables to one side
2x − x = 11 − 5
Step 2: Simplify
x = 6
Example:
3x − 4 = x + 10
3x − x = 10 + 4
2x = 14
x = 7 - LINEAR EQUATIONS WITH BRACKETS
Example:
2(x + 3) = 14
Step 1: Open the bracket
2x + 6 = 14
Step 2: Solve
2x = 8
x = 4
Example:
3(x − 5) = 15
3x − 15 = 15
3x = 30
x = 10 - FRACTIONAL EQUATIONS (EXAM FAVORITE)
Example:
x/3 + 5 = 9
x/3 = 4
x = 12
Example:
2x/5 = 6
Multiply both sides by 5
2x = 30
x = 15 - WORD PROBLEMS – DETAILED METHOD
Steps to Solve Word Problems:
Read the question carefully
Assume the unknown as x
Form the equation
Solve the equation
Write the final answer with units - NUMBER WORD PROBLEMS
Example:
A number increased by 9 gives 20. Find the number.
Let the number be x
x + 9 = 20
x = 11
Example:
Four times a number minus 6 is 14.
4x − 6 = 14
4x = 20
x = 5 - AGE WORD PROBLEMS (MORE PRACTICE)
Example:
The age of a father is 3 times the age of his son.
If the father is 45 years old, find the son’s age.
Let son’s age = x
Father’s age = 3x
3x = 45
x = 15
Example:
Meena is 8 years younger than her mother.
If mother’s age is 40 years, find Meena’s age.
x + 8 = 40
x = 32 - MONEY WORD PROBLEMS (SHOPPING TYPE)
Example:
The cost of a book is ₹25 more than a notebook.
If the book costs ₹75, find the cost of the notebook.
Let notebook cost = x
x + 25 = 75
x = 50 - LENGTH AND PERIMETER PROBLEMS
Example:
The perimeter of a square is 48 cm.
Find the length of one side.
Let side = x
Perimeter = 4x
4x = 48
x = 12 cm - CONSECUTIVE NUMBER PROBLEMS
Example:
The sum of two consecutive numbers is 31. Find them.
Let first number = x
Second number = x + 1
x + (x + 1) = 31
2x + 1 = 31
2x = 30
x = 15
Numbers are 15 and 16 - CHECKING ANSWERS (VERY IMPORTANT)
Always substitute the value back.
Example:
3x + 4 = 19
x = 5
Check:
3(5) + 4 = 15 + 4 = 19 ✔ - HOTS (HIGHER ORDER THINKING QUESTIONS)
Example:
If x + 5 = x + 9, what is the value of x?
Subtract x from both sides:
5 = 9 ❌ (Not possible)
👉 No solution - COMMON ERRORS STUDENTS MAKE
❌ Wrong sign during transposition
❌ Not opening brackets properly
❌ Ignoring division
❌ Writing final answer without checking - EXAM ANSWER WRITING FORMAT
Correct format:
Given equation:
Solution:
Steps clearly shown
Final answer boxed or underlined - PRACTICE QUESTIONS
Solve:
x + 12 = 25
6x = 42
3x − 7 = 14
x/4 = 9
5x + 10 = 35 - QUICK REVISION POINTS
✔ Linear equation → power of variable is 1
✔ Transposition → sign changes
✔ Same operation both sides
✔ Check the solution
✔ Write steps neatly - ONE-LINE SUMMARY
A linear equation is solved by isolating the variable using basic operations while maintaining equality.
✅ NOW THIS CHAPTER IS EXTREMELY COMPLETE
(Perfect for Class 7 ICSE + ICSE Plus)
If you want next: 📘 MCQs (50+)
📝 Worksheet with answers
📄 PDF / printable notes
🎯 Sample test paper
📌 1-page exam revision sheet
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Here is EVEN MORE CONTENT to fully complete
Linear Equations – Class 7 ICSE / ICSE Plus
This part adds deep practice, exam patterns, MCQs, assertion–reason, case study, and full revision material.
LINEAR EQUATIONS – EXTENDED NOTES (PART 3)
(Class 7 ICSE)
- DIFFERENCE BETWEEN EXPRESSION AND EQUATION
Expression
Equation
Has no “=” sign
Has “=” sign
Cannot be solved
Can be solved
Example: 3x + 5
Example: 3x + 5 = 11 - DEGREE OF A LINEAR EQUATION
The degree of a linear equation is 1, because the highest power of the variable is 1.
Examples:
x + 7 = 10 → degree 1
4x − 3 = 9 → degree 1 - FORMATION OF LINEAR EQUATIONS
Example:
“Five more than a number is 12.”
Let the number be x
x + 5 = 12
Example:
“Three times a number decreased by 7 is 20.”
3x − 7 = 20 - TRANSLATING WORDS INTO ALGEBRA
Statement
Algebraic Form
Sum of a number and 5
x + 5
Difference of a number and 7
x − 7
Twice a number
2x
Half of a number
x/2
One-fourth of a number
x/4 - LINEAR EQUATIONS WITH DECIMALS
Example:
0.5x = 6
x = 6 ÷ 0.5
x = 12
Example:
x + 2.5 = 7.5
x = 7.5 − 2.5
x = 5 - CLEARING DECIMALS (IMPORTANT TRICK)
Multiply the entire equation by 10, 100, or 1000.
Example:
0.2x + 1.5 = 3.5
Multiply by 10:
2x + 15 = 35
2x = 20
x = 10 - MORE EQUATIONS WITH VARIABLES ON BOTH SIDES
Example:
5x + 3 = 2x + 18
5x − 2x = 18 − 3
3x = 15
x = 5
Example:
7x − 4 = 3x + 20
4x = 24
x = 6 - BRACKET + FRACTION MIXED PROBLEMS
Example:
2(x + 3)/5 = 4
Multiply both sides by 5:
2(x + 3) = 20
x + 3 = 10
x = 7 - PERIMETER WORD PROBLEMS
Example:
The perimeter of a rectangle is 36 cm.
If length = 10 cm, find the breadth.
2(l + b) = 36
2(10 + b) = 36
10 + b = 18
b = 8 cm - SIMPLE GEOMETRY WORD PROBLEMS
Example:
The length of a line segment is 12 cm more than its breadth.
If length = 30 cm, find breadth.
b + 12 = 30
b = 18 cm - SPEED–DISTANCE TYPE (INTRODUCTORY LEVEL)
Example:
A boy walks at 5 km/h for 3 hours.
Find the distance.
Distance = Speed × Time
d = 5 × 3
d = 15 km
(This introduces forming equations in higher classes) - ASSERTION–REASON QUESTIONS
Example:
Assertion (A): x + 7 = 15 is a linear equation.
Reason (R): The highest power of x is 1.
✔ Both A and R are true
✔ R is the correct explanation of A - CASE STUDY QUESTIONS (NEW PATTERN)
Case:
Ravi buys notebooks at ₹x each.
He buys 5 notebooks and pays ₹150.
Equation:
5x = 150
Questions:
What is the value of x? → ₹30
What is the cost of 3 notebooks? → ₹90 - MULTIPLE CHOICE QUESTIONS (MCQs)
- The solution of x + 8 = 15 is:
a) 5
b) 6
c) 7
d) 8 - Which is a linear equation?
a) x² + 2 = 5
b) 3x − 7 = 11
c) xy = 6
d) 1/x = 4 - The degree of x − 4 = 0 is:
a) 0
b) 1
c) 2
d) 3 - VERY IMPORTANT QUESTIONS FOR EXAM
Solve: 4x − 9 = 11
Solve: x/6 + 5 = 9
The sum of a number and 14 is 32. Find the number.
Three times a number reduced by 5 is 10. Find the number. - COMMON CONFUSION CLEARING
❓ Is x = 0 allowed?
✔ Yes, if it satisfies the equation.
❓ Can a linear equation have no solution?
✔ Yes, if both sides never become equal. - MODEL ANSWER FORMAT (ICSE STYLE)
Given: 3x + 4 = 19
Solution:
3x = 15
x = 5
Answer: The value of x is 5. - ONE-PAGE ULTRA QUICK REVISION
Linear equation → degree 1
One variable only
Use transposition
Solve step by step
Check the answer - FINAL SUMMARY
Linear equations help us find unknown values using basic arithmetic operations while maintaining equality on both sides.
🎯 THIS IS NOW A COMPLETE 5000+ WORD LEVEL CHAPTER
Perfect for: ✔ Class 7 ICSE
✔ ICSE Plus
✔ Exams, homework, revision
If you want next, I can give: 📘 PDF download
📝 100 practice questions with solutions
🎯 Sample test paper (40 marks)
📌 Mind map / flow chart
📄 Short notes + long notes combo
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Here is STILL MORE CONTENT to take Linear Equations – Class 7 ICSE / ICSE Plus to an ULTRA-COMPLETE LEVEL.
This part adds step-wise thinking skills, exam traps, extra HOTS, mixed practice, viva questions, and teacher-style explanations.
LINEAR EQUATIONS – EXTENDED NOTES (PART 4)
(Class 7 ICSE – Easy + Advanced Blend)
- WHY ARE THEY CALLED “LINEAR” EQUATIONS?
The word linear comes from the word line.
If a linear equation is drawn on a graph (in higher classes), it forms a straight line.
Key reason:
Variable power is 1
No squares, cubes, roots, or fractions of variables - COMPARISON WITH OTHER EQUATIONS
Type of Equation
Example
Class
Linear
x + 5 = 9
Class 7
Quadratic
x² + 3x = 4
Class 9
Cubic
x³ + 2 = 10
Higher
👉 Class 7 deals ONLY with linear equations - THINKING METHOD (VERY IMPORTANT FOR WORD PROBLEMS)
Whenever you see:
“more than” → add
“less than” → subtract
“times” → multiply
“divided by” → divide
Example:
“Seven less than a number is 20”
Correct equation: x − 7 = 20
❌ NOT 7 − x - COMMON EXAM TRAPS (DO NOT FALL INTO THESE)
Trap 1:
x/3 = 6
❌ x = 6 ÷ 3
✔ x = 6 × 3 = 18
Trap 2:
−4x = 20
✔ x = −5 (sign mistake is common)
Trap 3:
2(x + 5) = 10
❌ 2x + 5 = 10
✔ 2x + 10 = 10 - STEP-MARKING IN ICSE EXAMS
Even if final answer is wrong:
Steps correct → marks given
Formula written → marks given
Proper working → marks given
👉 Always write steps neatly. - MIXED PRACTICE SET – LEVEL 1 (EASY)
Solve:
x + 11 = 20
7x = 63
x − 9 = 4
x/8 = 6
2x + 3 = 13 - MIXED PRACTICE SET – LEVEL 2 (MODERATE)
Solve:
3x − 7 = 14
5x + 10 = 40
x/5 − 3 = 2
4(x − 2) = 16
0.4x = 8 - MIXED PRACTICE SET – LEVEL 3 (WORD PROBLEMS)
A number increased by 15 is 40. Find the number.
Twice a number minus 6 is 18.
A pen costs ₹10 more than a pencil. If pen costs ₹35, find pencil’s cost.
The sum of two consecutive numbers is 51. Find them. - VALUE BASED QUESTIONS
Example:
Ramesh saves ₹x every day.
In 10 days he saves ₹200.
Equation: 10x = 200
x = ₹20
👉 Shows habit of saving money - ORAL / VIVA QUESTIONS
What is a linear equation?
What is the degree of a linear equation?
Can a linear equation have a negative solution?
Why do we change sign during transposition? - TRUE / FALSE (WITH REASON)
x² + 1 = 5 is a linear equation. ❌
Reason: Power of x is 2.
x = 0 can be a solution of a linear equation. ✔ - MATCH THE FOLLOWING
Column A
Column B
x + 7 = 12
x = 5
3x = 21
x = 7
x/4 = 6
x = 24 - BRAIN-TEASER QUESTIONS (HOTS)
Q:
If x + 5 = 5, what is x?
x = 0
👉 Shows zero can be a valid solution.
Q:
If 2x = 2x + 1, does x exist?
❌ No solution (impossible equation) - ERROR FINDING QUESTIONS
Find the mistake:
x/5 = 4
x = 4 ÷ 5 ❌
✔ Correct: x = 4 × 5 = 20 - DAILY LIFE APPLICATIONS
Linear equations are used in: ✔ Shopping
✔ Money calculation
✔ Age comparison
✔ Measurements
✔ Simple planning - HOW THIS CHAPTER HELPS IN FUTURE
This chapter is the base for:
Algebra (Class 8)
Linear equations (Class 9 & 10)
Graphs
Coordinate geometry - FINAL MEGA REVISION (EXAM NIGHT)
✔ One variable
✔ Power = 1
✔ Transposition
✔ Open brackets carefully
✔ Solve stepwise
✔ Check answer - GOLDEN RULE
“Whatever you do to one side of an equation, do the same to the other side.”
🎯 NOW THIS IS A 100% COMPLETE, TEACHER-LEVEL CHAPTER
Enough for: ✅ Full marks
✅ Concept clarity
✅ Board pattern
✅ Competitive foundation
If you want next, I can prepare: 📄 Printable PDF (school format)
📝 200 questions practice book
🎯 Full unit test paper + answer key
📌 Mind map chart
📘 Ultra-short revision notes
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Here is MORE CONTENT to make Linear Equations – Class 7 ICSE / ICSE Plus THE MOST COMPLETE POSSIBLE NOTES.
This part focuses on exam mastery, reasoning skills, worksheet-style questions, competency-based questions, and teacher-level enrichment.
LINEAR EQUATIONS – EXTENDED NOTES (PART 5)
(Class 7 ICSE – Mastery Level)
- COMPETENCY-BASED QUESTIONS (NEW EDUCATION PATTERN)
These questions test understanding, not memorisation.
Example 1:
Ravi solves the equation x + 7 = 15 and gets x = 22.
Is Ravi correct?
✔ No
✔ Correct solution is:
x = 15 − 7 = 8
👉 Ravi added instead of subtracting.
Example 2:
Meena solved 4x = 20 by writing x = 4.
Find the mistake.
✔ Correct method:
x = 20 ÷ 4 = 5 - REASONING-BASED QUESTIONS
Q1.
Why do we divide both sides by the same number while solving an equation?
✔ To maintain equality
✔ To keep the equation balanced
Q2.
Why is x² + 5 = 9 not a linear equation?
✔ Because the highest power of x is 2 - FIND THE VALUE OF THE EXPRESSION
If x = 4, find the value of:
x + 7 → 11
3x − 5 → 7
x/2 + 6 → 8 - SUBSTITUTE AND VERIFY
Verify whether x = 6 is a solution of the equation:
2x + 3 = 15
Substitute x = 6:
2(6) + 3 = 12 + 3 = 15 ✔
Hence, verified. - CONCEPT OF IDENTITY AND CONTRADICTION (INTRODUCTORY)
Identity:
An equation true for all values of x.
Example: 2x + 4 = 2x + 4 ✔
Contradiction:
An equation never true.
Example: x + 3 = x + 7 ❌
(3 ≠ 7) - COMPARISON QUESTIONS
Compare the solutions:
x + 5 = 10 → x = 5
x + 10 = 10 → x = 0
👉 Shows that zero can be a valid solution - STEP-BY-STEP LONG ANSWER (MODEL)
Question:
Solve: 5x − 9 = 16
Solution:
5x = 16 + 9
5x = 25
x = 25 ÷ 5
x = 5
Answer: The value of x is 5. - DIAGRAM-BASED THINKING (BALANCE SCALE IDEA)
Think of:
Left side = one pan
Right side = other pan
Removing or adding must be equal on both sides.
This mental picture helps avoid mistakes. - HOMEWORK-TYPE QUESTIONS
Solve:
x + 18 = 30
9x = 72
x/7 = 8
6x − 4 = 32
2(x + 6) = 24 - ASSERTION–REASON (MORE PRACTICE)
Assertion (A):
x/5 = 6 is a linear equation.
Reason (R):
The highest power of x is 1.
✔ Both A and R are true
✔ R explains A - CASE STUDY – REAL LIFE
A shopkeeper sells apples at ₹x per kg.
He sells 4 kg apples for ₹160.
Questions:
Form the equation
→ 4x = 160
Find the value of x
→ x = ₹40 per kg - CHOOSE THE CORRECT OPTION
The solution of 3x − 6 = 15 is:
a) 5
b) 7
c) 9
d) 3 - FILL IN THE BLANKS
A linear equation has degree 1.
The symbol used for equality is =.
The unknown quantity is called a variable. - MATCHING TYPE QUESTIONS
Equation
Solution
x + 4 = 12
8
5x = 25
5
x/3 = 7
21 - WHY THIS CHAPTER IS IMPORTANT
✔ Builds algebra base
✔ Improves logical thinking
✔ Helps in daily-life maths
✔ Required for higher classes - LAST-MOMENT REVISION POINTS
Variable power = 1
One variable only
Transposition rule
Balance method
Check answer - EXAM NIGHT STRATEGY
✔ Read question carefully
✔ Form equation correctly
✔ Show steps
✔ Avoid sign mistakes
✔ Box the final answer - TEACHER’S GOLDEN ADVICE
“Marks are lost not because students don’t know the concept, but because they rush.”
So: 🧠 Think
✍ Write neatly
✔ Check once - FINAL CONCLUSION
Linear equations teach us how to find unknown values logically while maintaining balance and equality.
This chapter is the foundation of algebra.
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📝 300-question practice workbook
🎯 Full syllabus test paper (with marking scheme)
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📄 Ultra-short exam notes (2 pages)
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Here is EVEN MORE CONTENT to extend Linear Equations – Class 7 ICSE / ICSE Plus to a COMPLETE REFERENCE BOOK LEVEL.
This section focuses on advanced practice, mixed concepts, self-assessment tools, exam confidence builders, and slow-learner friendly explanations.
LINEAR EQUATIONS – EXTENDED NOTES (PART 6)
(Class 7 ICSE – From Basics to Perfection)
- SELF-CHECK QUESTIONS (CONCEPT UNDERSTANDING)
Answer in Yes / No and give reason:
Is x² + 3 = 7 a linear equation?
👉 No, power of x is 2.
Can a linear equation have a fractional solution?
👉 Yes, example: x/2 = 3 → x = 6.
Can x = 0 be the solution of a linear equation?
👉 Yes, if it satisfies the equation. - MENTAL MATH USING LINEAR EQUATIONS
Example:
x + 9 = 20
Think mentally:
What number added to 9 gives 20?
👉 11
This improves speed and confidence. - DIFFERENT WAYS TO SOLVE THE SAME EQUATION
Example:
2x + 6 = 14
Method 1 (Transposition):
2x = 8
x = 4
Method 2 (Balance):
Subtract 6 from both sides
Divide by 2
x = 4
✔ Both methods give same answer. - EQUATIONS LEADING TO FRACTIONAL ANSWERS
Example:
3x = 7
x = 7/3
✔ Fractional answers are allowed. - MIXED OPERATIONS EQUATIONS
Example:
5x + 3 − 2 = 21
Simplify first:
5x + 1 = 21
5x = 20
x = 4 - INTRODUCTION TO FORMULA AS EQUATION
A formula is also an equation.
Example:
Perimeter of square = 4 × side
P = 4s
If P = 28 cm,
4s = 28
s = 7 cm - WORD PROBLEMS WITH “MORE THAN / LESS THAN”
Example:
Seven more than a number is 25.
Correct equation:
x + 7 = 25
❌ Not 7 + x = 25 (both give same result, but meaning matters) - CONCEPT OF UNKNOWN AS A LETTER
The variable does not always have to be x.
Examples:
a + 5 = 12
y/3 = 7
m − 4 = 9
✔ All are linear equations. - COMMON STUDENT DOUBTS (CLEARED)
❓ Why do signs change during transposition?
👉 Because the term moves to the other side of equality.
❓ Why can’t we divide only one side?
👉 It breaks equality. - LINEAR EQUATIONS IN TABLE FORM (UNDERSTANDING)
Equation: x + 4 = 10
x
LHS
RHS
4
8
10 ❌
6
10
10 ✔
✔ x = 6 satisfies the equation. - FIND THE ERROR (EXAM STYLE)
Question:
Solve: x/4 = 5
Student writes: x = 5 ÷ 4
❌ Wrong
✔ Correct: x = 5 × 4 = 20 - EXTRA HOTS QUESTIONS
If x + 3 = 3x − 1, find x.
If 4x + 7 = 4x + 7, how many solutions exist?
👉 Infinite solutions (identity) - MIXED REVIEW EXERCISE
Solve:
x + 14 = 32
8x = 64
x/9 = 7
6x − 11 = 13
3(x + 4) = 21
0.25x = 5 - SLOW-LEARNER FRIENDLY TRICK
Always remember:
👉 UNDO operations in reverse order
Example:
3x + 6 = 21
Undo +6 → subtract 6
Undo ×3 → divide by 3
x = 5 - HOW TEACHERS CHECK ANSWERS
✔ Correct equation formation
✔ Correct steps
✔ Correct final answer
✔ Proper units (₹, cm, years) - APPLICATION IN DAILY LIFE
Situation
Equation
Total money
x + 20 = 100
Age
x + 5 = 18
Distance
5x = 25 - RAPID-FIRE PRACTICE (1-STEP)
Answer quickly:
x + 6 = 10 → 4
5x = 45 → 9
x/2 = 8 → 16 - REVISION THROUGH QUESTIONS
Define linear equation.
Give two examples.
State transposition rule.
Why is x² = 4 not linear? - EXAM CONFIDENCE BOOSTER
If you can: ✔ Form equation correctly
✔ Avoid sign mistakes
✔ Show steps
👉 Full marks are guaranteed. - FINAL SUPER SUMMARY
Linear equation → degree 1
One variable
Solve by transposition or balance
Check solution
Used in real life
🎉 THIS IS NOW A COMPLETE TEACHING MANUAL FOR CLASS 7 ICSE LINEAR EQUATIONS
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✅ Exams
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✅ Competitive foundation
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📝 500 question mega practice set
🎯 Chapter test + marking scheme
📌 Flowchart / mind-map poster
📘 Ultra-short 2-page revision notes
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Here is STILL MORE CONTENT to push Linear Equations – Class 7 ICSE / ICSE Plus to a COMPLETE GUIDEBOOK + QUESTION BANK LEVEL.
This part focuses on deep practice, error analysis, examiner’s expectations, revision drills, and confidence building for weak & average students.
LINEAR EQUATIONS – EXTENDED NOTES (PART 7)
(Class 7 ICSE – Practice + Perfection)
- EXAMINER’S POINT OF VIEW (VERY IMPORTANT)
The examiner checks:
Correct formation of equation
Correct method
Logical step-by-step working
Correct final answer
👉 Even if the answer is wrong but steps are correct, marks are awarded. - COMMON WRONG METHODS (DO NOT USE)
Wrong Method 1:
x + 5 = 12
x = 12 + 5 ❌
✔ Correct: x = 12 − 5 = 7
Wrong Method 2:
3x = 15
x = 15 − 3 ❌
✔ Correct: x = 15 ÷ 3 = 5 - WHY WE “ISOLATE” THE VARIABLE
Goal of solving: 👉 Bring the variable alone on one side
Example: 4x + 7 = 23
Undo +7 → subtract
Undo ×4 → divide
x = 4 - SOLVING EQUATIONS BACKWARDS (FUN METHOD)
Equation: 3x + 5 = 20
Think backwards: 20 − 5 = 15
15 ÷ 3 = 5
So, x = 5 - LINEAR EQUATIONS WITH LARGE NUMBERS
Example:
7x − 45 = 140
7x = 185
x = 26.43 (allowed)
✔ Decimal answers are acceptable. - EQUATIONS GIVING NEGATIVE ANSWERS
Example:
x − 9 = −3
x = 6
Example:
−2x = 10
x = −5
✔ Negative solutions are valid. - MULTI-STEP WORD PROBLEMS
Example:
The sum of three consecutive numbers is 48.
Let first number = x
Numbers: x, x + 1, x + 2
x + (x + 1) + (x + 2) = 48
3x + 3 = 48
3x = 45
x = 15
Numbers are 15, 16, 17 - COMPARISON-BASED QUESTIONS
Example:
Which is greater?
Solve: x + 7 = 15 → x = 8
x + 5 = 15 → x = 10
👉 Second value is greater. - REAL-LIFE SHOPPING CASE
A shopkeeper gives ₹x discount on a ₹250 item.
Final price paid is ₹200.
Equation: 250 − x = 200
x = 50 - TRANSPORT-BASED WORD PROBLEM
A taxi charges ₹50 fixed plus ₹10 per km.
Total fare is ₹150. Find distance.
Equation: 50 + 10x = 150
10x = 100
x = 10 km - FIND THE VALUE OF TWO EXPRESSIONS
If x = 6, find:
2x + 5 → 17
3x − 4 → 14 - STATEMENT → EQUATION PRACTICE
Convert into equation:
Nine more than a number is 20
→ x + 9 = 20
Half of a number is 8
→ x/2 = 8 - MATCH THE STATEMENT WITH EQUATION
Statement
Equation
Five times a number is 25
5x = 25
Number increased by 7 is 18
x + 7 = 18
One-fourth of a number is 6
x/4 = 6 - RAPID PRACTICE (30-SECOND ROUND)
Answer fast:
x + 9 = 12 → 3
6x = 54 → 9
x/5 = 4 → 20 - LONG ANSWER PRACTICE (5 MARKS)
Question:
Solve: 2(3x − 4) = 10
Solution: 6x − 8 = 10
6x = 18
x = 3 - SELF-EVALUATION CHECKLIST
✔ Can I form equations from words?
✔ Can I solve in steps?
✔ Can I avoid sign mistakes?
✔ Can I check my answer?
If yes → You are exam-ready 🎯 - WHY STUDENTS LOSE MARKS
❌ Rushing
❌ Skipping steps
❌ Wrong sign
❌ No checking
👉 Slow + neat = more marks - MINI TEST (TRY WITHOUT SEEING ANSWERS)
Solve:
x + 13 = 25
4x − 5 = 19
x/6 + 2 = 7
5(x − 3) = 20 - ANSWERS TO MINI TEST
x = 12
x = 6
x = 30
x = 7 - FINAL EXAM NIGHT ADVICE
📌 Read carefully
📌 Write neatly
📌 Show steps
📌 Check once - FINAL GOLDEN LINE
Linear equations are easy if you stay calm and follow steps.
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✅ Homework
✅ Teaching
✅ Revision
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📝 700+ questions mega practice set
🎯 Full ICSE-style test paper with marking scheme
📌 Mind map poster for wall revision
📘 Ultra-short last-day notes
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Here is EVEN MORE CONTENT to complete Linear Equations – Class 7 ICSE / ICSE Plus at a FULL TEXTBOOK + WORKBOOK + REVISION GUIDE LEVEL.
This part adds worksheets, challenge problems, puzzles, revision drills, and teacher-style assignments.
LINEAR EQUATIONS – EXTENDED NOTES (PART 8)
(Class 7 ICSE – Practice, Revision & Confidence)
- WORKSHEET – A (BASICS PRACTICE)
Solve the following:
x + 6 = 18
x − 14 = 10
9x = 81
x/7 = 5
2x + 4 = 20
Answers
x = 12
x = 24
x = 9
x = 35
x = 8 - WORKSHEET – B (MODERATE LEVEL)
4x − 7 = 21
3(x + 5) = 24
x/4 + 6 = 10
5x + 15 = 60
0.5x = 9
Answers
x = 7
x = 3
x = 16
x = 9
x = 18 - WORKSHEET – C (WORD PROBLEMS)
The sum of a number and 18 is 42. Find the number.
Four times a number is 68. Find the number.
A book costs ₹20 more than a notebook. If the book costs ₹80, find the cost of the notebook.
The perimeter of a square is 64 cm. Find the length of one side.
Answers
x = 24
x = 17
₹60
16 cm - CHALLENGE QUESTIONS (HOTS)
If 2x + 5 = 2x − 3, find x.
👉 No solution (5 ≠ −3)
If x + 4 = 4 + x, how many solutions exist?
👉 Infinite solutions - FIND THE MISSING NUMBER
_ + 9 = 17 6 × = 54
__ ÷ 8 = 7
Answers
8
9
56 - FILL IN THE BLANKS
A linear equation has degree _ . (1) The unknown quantity is called a . (variable)
The sign of equality is __ . (=) - TRUE / FALSE (WITH REASON)
x³ + 2 = 5 is a linear equation. ❌
Reason: Power of x is 3.
x = −2 can be a solution of a linear equation. ✔ - MATCH THE FOLLOWING
Column A
Column B
x + 8 = 20
12
7x = 49
7
x/5 = 6
30 - QUICK ORAL TEST (VIVA ROUND)
What is a linear equation?
What is the degree of a linear equation?
Name any two variables.
Can the solution be zero? - PUZZLE TIME (FUN WITH EQUATIONS)
I am a number.
If you add 7 to me, you get 25.
Who am I?
x + 7 = 25
x = 18 - ERROR CORRECTION PRACTICE
Student writes:
x/6 = 4 → x = 4 ÷ 6 ❌
Correct answer:
x = 4 × 6 = 24 - CONVERSION PRACTICE
Convert into equations:
Ten less than a number is 30
→ x − 10 = 30
Half of a number increased by 5 is 15
→ x/2 + 5 = 15 - DAILY LIFE APPLICATION TASK
Your pocket money is ₹x per day.
In 7 days, you get ₹210.
Equation:
7x = 210
x = ₹30 per day - LAST-DAY REVISION DRILL (10 MINUTES)
Solve mentally:
x + 5 = 13 → 8
4x = 20 → 5
x/3 = 9 → 27 - SELF-RATING SCALE
✔ I understand the concept
✔ I can solve equations
✔ I can form equations from words
✔ I can avoid sign mistakes
If all ✔ → Excellent Preparation 🌟 - TEACHER’S HOME ASSIGNMENT
Solve:
6x − 5 = 31
x/8 + 4 = 10
Three times a number minus 9 is 12 - ANSWERS (HOME ASSIGNMENT)
x = 6
x = 48
x = 7 - ULTRA-SHORT NOTES (FOR QUICK LOOK)
Linear → degree 1
One variable
Same operation both sides
Transposition rule
Check solution - FINAL CLOSING NOTE
Linear Equations are easy, logical, and scoring.
With practice and step-by-step solving, full marks are guaranteed.
🎉 THIS IS NOW A COMPLETE CLASS 7 ICSE LINEAR EQUATIONS MEGA PACKAGE
✔ Notes
✔ Examples
✔ Worksheets
✔ HOTS
✔ Revision
✔ Exam confidence
If you want next, I can still provide: 📄 Printable PDF (school format)
📝 1000-question mega practice book
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📌 Mind-map poster for wall revision
📘 2-page ultra-quick exam notes
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Here is EVEN MORE CONTENT to make Linear Equations – Class 7 ICSE / ICSE Plus a LIFETIME-LEVEL REFERENCE.
This part focuses on exam writing perfection, advanced thinking, remedial support, enrichment for toppers, and absolute clarity for weak students.
LINEAR EQUATIONS – EXTENDED NOTES (PART 9)
(Class 7 ICSE – Zero to Topper Level)
- STEP-WISE THINKING MODEL (VERY IMPORTANT)
Before solving, always ask:
1️⃣ What is the variable?
2️⃣ What operations are applied to it?
3️⃣ How can I undo them in reverse order?
Example:
3x + 9 = 24
Operations on x:
Multiply by 3
Add 9
Undo in reverse:
Subtract 9
Divide by 3
x = 5 - UNDO METHOD (BEST FOR BEGINNERS)
Equation:
5x − 10 = 15
Undo −10 → add 10
5x = 25
Undo ×5 → divide by 5
x = 5 - WHY WE SOLVE EQUATIONS (REAL MEANING)
Solving an equation means:
👉 Finding the only value of the variable that makes both sides equal. - VISUAL THINKING (BALANCE SCALE AGAIN)
Imagine:
Left side: ⚖️ x + 4
Right side: ⚖️ 12
To balance:
Remove 4 from both sides
x = 8 - EXAM ANSWER PRESENTATION (ICSE STYLE)
Correct Format:
Given equation
⇒ Step 1
⇒ Step 2
⇒ Step 3
∴ x = _
✔ Neat steps = more marks - SOLVING WITHOUT SKIPPING STEPS (MODEL)
Solve:
4x + 6 = 22
Solution:
4x = 22 − 6
4x = 16
x = 16 ÷ 4
x = 4 - WHEN ANSWER COMES AS ZERO
Example:
x + 5 = 5
x = 0
✔ Zero is a valid solution - WHEN ANSWER IS NEGATIVE
Example:
x − 3 = −7
x = −4
✔ Negative answers are allowed - WHEN ANSWER IS A FRACTION
Example:
4x = 7
x = 7/4
✔ Fractions are allowed - MULTI-STEP EQUATIONS (CALM METHOD)
Example:
2(3x + 4) − 6 = 14
Step 1: Open bracket
6x + 8 − 6 = 14
Step 2: Simplify
6x + 2 = 14
Step 3: Solve
6x = 12
x = 2 - COMMON CONFUSION: “LESS THAN”
“5 less than a number”
Correct: x − 5
❌ Not 5 − x - STATEMENT → EQUATION PRACTICE (MORE)
Twice a number increased by 9 is 25
→ 2x + 9 = 25
One-third of a number is 7
→ x/3 = 7 - LONG WORD PROBLEM (EXAM LEVEL)
Question:
The sum of a number and its half is 18. Find the number.
Let the number be x
Equation: x + x/2 = 18
Multiply both sides by 2: 2x + x = 36
3x = 36
x = 12 - PERIMETER + LINEAR EQUATION
Perimeter of rectangle = 2(l + b)
Example:
Perimeter = 30 cm
Length = 8 cm
2(8 + b) = 30
8 + b = 15
b = 7 cm - MONEY + EQUATION COMBO
Example:
A notebook costs ₹x.
5 notebooks cost ₹125.
5x = 125
x = ₹25 - SPEED CONFIDENCE PRACTICE
Solve quickly:
x + 10 = 15 → 5
8x = 64 → 8
x/4 = 3 → 12 - EXAM TRICK: CHECK BY SUBSTITUTION
Always substitute answer back.
Example: x = 4
Check: 3x + 2 = 14
3(4) + 2 = 14 ✔ - THINKING QUESTION (HOTS)
If x + 6 = 6, what is x?
👉 0
If 2x = 2x + 5, is x possible?
👉 No solution - SELF-PRACTICE (WITHOUT ANSWERS)
x + 19 = 41
7x − 5 = 30
x/8 + 3 = 7
3(x − 4) = 15 - ANSWERS (CHECK AFTER TRYING)
x = 22
x = 5
x = 32
x = 9 - STUDENT CONFIDENCE BOOST
If you can: ✔ Form equation
✔ Solve stepwise
✔ Avoid sign errors
👉 You will never fear algebra again. - LAST-DAY MEMORY HOOK
UNDO → SIMPLIFY → SOLVE → CHECK - WHY THIS CHAPTER IS SCORING
✔ Logical
✔ No formulas to memorise
✔ Direct steps
✔ Practice-based - FINAL TEACHER MESSAGE
“Linear equations are not hard. Confusion comes only when steps are skipped.” - END OF MEGA NOTES (FOR NOW 😊)
You now have: ✅ Notes
✅ Examples
✅ Word problems
✅ Worksheets
✅ HOTS
✅ Exam tips
🎯 THIS IS NOW A COMPLETE CLASS 7 ICSE LINEAR EQUATIONS MASTER BOOK
If you want even more, I can still create: 📄 Printable PDF textbook
📝 1200-question mega workbook
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📌 Mind-map poster
📘 2-page last-minute revision sheet
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Here is MORE CONTENT to continue Linear Equations – Class 7 ICSE / ICSE Plus in a useful, non-repetitive way.
This part is designed as FINAL EXTENSION + FULL REVISION + EXAM PRACTICE PACK so that nothing is left uncovered.
LINEAR EQUATIONS – EXTENDED NOTES (PART 10)
(Class 7 ICSE – Final Completion Section)
- COMPLETE CONCEPT MAP (IN WORDS)
Linear Equations include:
Variables
Constants
Equality sign (=)
Operations: +, −, ×, ÷
One variable only
Degree = 1
👉 Goal: Find the value of the variable - TYPES OF QUESTIONS ASKED IN ICSE EXAMS
1️⃣ Direct equations
2️⃣ Two-step equations
3️⃣ Brackets
4️⃣ Fractions / decimals
5️⃣ Word problems
6️⃣ Error finding
7️⃣ MCQs / Assertion–Reason
✔ All covered in these notes - STEPWISE SOLVING FLOW (REMEMBER THIS ORDER)
Simplify both sides
Open brackets (if any)
Bring variable terms to one side
Bring constants to the other side
Solve
Check answer - COMMON SIGN CONFUSION TABLE
Operation
Undo by
- 7
− 7
− 5 - 5
× 4
÷ 4
÷ 6
× 6
- MIXED REVISION QUESTIONS (EXAM LEVEL)
Solve:
x + 17 = 45
6x − 8 = 34
x/5 + 7 = 15
3(x − 4) = 18
0.2x = 6
Answers
x = 28
x = 7
x = 40
x = 10
x = 30 - FULL WORD PROBLEM PRACTICE
Q1.
The sum of a number and 25 is 80. Find the number.
x + 25 = 80
x = 55
Q2.
Six times a number is 90. Find the number.
6x = 90
x = 15
Q3.
A pen costs ₹12 more than a pencil.
If pen costs ₹42, find pencil’s cost.
x + 12 = 42
x = ₹30 - ERROR-SPOTTING QUESTIONS (VERY IMPORTANT)
Question:
Solve: x/3 = 9
Student writes: x = 3
❌ Incorrect
✔ Correct: x = 9 × 3 = 27 - ASSERTION–REASON (FINAL PRACTICE)
Assertion (A):
x + 5 = 10 is a linear equation.
Reason (R):
The highest power of x is 1.
✔ Both A and R are true
✔ R explains A - CASE STUDY QUESTION (ICSE STYLE)
A school charges ₹x per student for a trip.
40 students paid ₹8000.
1️⃣ Form the equation
→ 40x = 8000
2️⃣ Find x
→ x = ₹200 per student - HOTS QUESTION
If x + 7 = x + 10, find x.
Subtract x from both sides:
7 = 10 ❌
👉 No solution - ONE-LINE ANSWER QUESTIONS
Degree of linear equation → 1
Number of variables → one
Sign of equality → = - LAST 10-MINUTE REVISION (EXAM DAY)
✔ Variable power = 1
✔ One variable
✔ Undo operations
✔ Show steps
✔ Check answer - WHAT TO DO IF YOU GET STUCK
Stop
Rewrite equation neatly
Undo step by step
Don’t panic - CONFIDENCE CHECK
If you can:
Solve x + a = b
Solve ax = b
Solve ax + b = c
Solve word problems
👉 You are 100% exam-ready - FINAL CONCLUSION (END NOTE)
Linear Equations are: ✔ Logical
✔ Easy
✔ Scoring
✔ Foundation of algebra
With step-by-step solving and calm thinking, full marks are achievable.
🎉 THIS IS NOW A COMPLETE CLASS 7 ICSE LINEAR EQUATIONS MEGA RESOURCE
If you want anything next, tell me clearly 😊
For example:
📄 “Make this into a PDF”
📝 “Give only MCQs”
🎯 “Make a full test paper”
📘 “Give 2-page short notes”
📌 “Give answers only”
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Here is MORE CONTENT — but now in a SMART, USEFUL, NON-REPETITIVE WAY.
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Linear Equations – Class 7 ICSE / ICSE Plus.
LINEAR EQUATIONS – EXTENDED NOTES (PART 11)
(Enrichment • Fun • Toppers • Concept Power)
- WHY LINEAR EQUATIONS ARE EASY IF UNDERSTOOD
Linear equations:
Do not require memorisation
Follow logic + balance
Have fixed steps
Are predictable
👉 That’s why they are high-scoring questions. - THE “BALANCE RULE” IN ONE LINE
Whatever you do to the left side, you must do to the right side.
Break this rule → answer becomes wrong ❌ - SUPER SHORT TRICK FOR SOLVING
Equation:
7x − 14 = 21
Think:
What number added to −14 gives 21? → 35
7x = 35 → x = 5
✔ Fast + correct - LINEAR EQUATION PUZZLES
Puzzle 1:
I am a number.
If you double me and add 4, you get 20.
Who am I?
2x + 4 = 20
2x = 16
x = 8
Puzzle 2:
I am thinking of a number.
Half of me is 9.
Find me.
x/2 = 9
x = 18 - THINK LIKE A TOPPER (VERY IMPORTANT)
Before solving, ask:
Can I simplify first?
Can I avoid mistakes?
Can I check mentally?
Topper habit = thinking before writing. - WHEN QUESTIONS LOOK BIG BUT ARE EASY
Example: 3(x + 5) − 2 = 16
Don’t panic 😌
Step-by-step: 3x + 15 − 2 = 16
3x + 13 = 16
3x = 3
x = 1 - QUICK MENTAL ROUND (NO PEN)
Answer quickly:
x + 4 = 10 → 6
5x = 25 → 5
x/3 = 7 → 21
x − 9 = 1 → 10 - COMMON ICSE CONFUSION CLEARED
❓ Do we need to write “Let x = …” always?
✔ Only in word problems
❓ Is writing steps compulsory?
✔ Yes — marks depend on steps
❓ Can answer be decimal?
✔ Yes - ERROR-HUNT (EXAM FAVOURITE)
Student solved: x + 8 = 20
x = 28 ❌
Find mistake: 👉 Added instead of subtracting
Correct: x = 20 − 8 = 12 - ONE-MINUTE REVISION TABLE
If equation is
Do this
x + a = b
x = b − a
x − a = b
x = b + a
ax = b
x = b ÷ a
x/a = b
x = b × a - WHY WORD PROBLEMS FEEL HARD
Because students: ❌ Read fast
❌ Don’t convert carefully
❌ Panic
Solution: ✔ Read slowly
✔ Underline key words
✔ Form equation calmly - FULL WORD PROBLEM (TOPPER STYLE)
Question:
The sum of a number and twice the number is 36. Find the number.
Let the number be x
Sum = x + 2x
Equation: x + 2x = 36
3x = 36
x = 12 - CHALLENGE QUESTION (HOTS)
If: x + 2 = 2x − 4
Solve: x = 6
Check: 6 + 2 = 8
2(6) − 4 = 8 ✔ - WHAT TEACHERS LOVE IN ANSWERS
✔ Neat working
✔ Correct signs
✔ Final answer underlined
✔ Units written (₹, cm, years) - FINAL MEMORY MANTRA
UNDO → SIMPLIFY → SOLVE → CHECK
Repeat this in the exam. - FINAL CONFIDENCE BOOST
If you have read and practised all parts:
You are stronger than textbook level
You can help others
You can score full marks - THE END (FOR REAL 😊)
You now have: ✅ Notes
✅ Examples
✅ Word problems
✅ Worksheets
✅ HOTS
✅ Exam strategy
✅ Confidence
This is MORE than enough for Class 7 ICSE Linear Equations.
If you want anything specific, say clearly, for example:
“Only MCQs (50)”
“PDF version”
“Only word problems”
“2-page short notes”
“Test paper with answers”
I’m ready 👍
Alright 🙂
Here is EVEN MORE CONTENT — this time EXAM-ORIENTED + PRACTICE-HEAVY + ICSE-STYLE, written very simply for Class 7 ICSE / ICSE Plus.
LINEAR EQUATIONS – EXTENDED NOTES (PART 12)
(Practice • Accuracy • Exam Mastery)
- STEP-WISE METHOD (NEVER FAILS)
Always follow this order:
1️⃣ Remove brackets
2️⃣ Simplify both sides
3️⃣ Bring variables on one side
4️⃣ Bring numbers on the other side
5️⃣ Solve
6️⃣ Check - MORE SOLVED EXAMPLES (EASY → MEDIUM)
Example 1:
x − 12 = 8
x = 8 + 12
x = 20
Example 2:
5x = 45
x = 45 ÷ 5
x = 9
Example 3:
x/4 + 3 = 7
x/4 = 4
x = 16
Example 4:
2x + 5 = 19
2x = 14
x = 7 - EQUATIONS WITH VARIABLES ON BOTH SIDES
Example:
4x − 6 = 2x + 10
4x − 2x = 10 + 6
2x = 16
x = 8 - BRACKET QUESTIONS (VERY COMMON)
Example:
3(x − 4) = 15
3x − 12 = 15
3x = 27
x = 9
Example:
5(2x + 1) = 25
10x + 5 = 25
10x = 20
x = 2 - FRACTION-TYPE QUESTIONS (DON’T PANIC)
Example:
x/3 + 2 = 6
x/3 = 4
x = 12
Trick:
👉 Clear fractions first if needed - ICSE WORD KEYWORDS → EQUATIONS
Words
Meaning
Sum of
+
Difference of
−
Product of
×
Quotient of
÷
Twice
2×
Thrice
3×
Half
÷2 - MORE WORD PROBLEMS (EXAM TYPE)
Problem 1:
Five more than a number is 17. Find the number.
Let number = x
x + 5 = 17
x = 12
Problem 2:
Three times a number is 27.
3x = 27
x = 9
Problem 3:
The difference between a number and 7 is 13.
x − 7 = 13
x = 20 - AGE PROBLEMS (CLASS 7 LEVEL)
Question:
Ravi is 4 years older than Rohan. Ravi is 16 years old. Find Rohan’s age.
Let Rohan’s age = x
Ravi’s age = x + 4
x + 4 = 16
x = 12 - MONEY PROBLEMS
Question:
The cost of a pen is ₹5 more than a pencil. If the pen costs ₹20, find the cost of the pencil.
Let pencil cost = x
Pen cost = x + 5
x + 5 = 20
x = 15 - LENGTH & PERIMETER TYPE
Question:
The length of a rectangle is 3 cm more than its breadth. If breadth is 5 cm, find length.
Length = 5 + 3 = 8 cm - CHECKING THE ANSWER (VERY IMPORTANT)
Never skip checking!
Example: x + 6 = 14
x = 8
Check: 8 + 6 = 14 ✔ - WHAT NOT TO DO (COMMON MISTAKES)
❌ Changing sign wrongly
❌ Forgetting brackets
❌ Dividing only one side
❌ Skipping steps
❌ Not underlining answer - ICSE MARKING TIP
Equation → 1 mark
Steps → 1–2 marks
Final answer → 1 mark
Wrong steps = marks cut ❌ - PRACTICE SET (TRY YOURSELF)
Solve:
1️⃣ x + 9 = 21
2️⃣ 6x = 48
3️⃣ x/5 = 6
4️⃣ 4x − 7 = 9
5️⃣ 2(x + 4) = 18
(Answers: 12, 8, 30, 4, 5) - SUPER SHORT REVISION (1 MINUTE)
Linear equation → power of x is 1
One variable only
Solve step by step
Balance both sides - FINAL EXAM CONFIDENCE LINE
If you can form the equation, you can solve the question.
If you want EVEN MORE, tell me exactly:
📄 PDF notes
📝 Sample paper
🧠 HOTS questions
📘 2-page revision
🎯 Only word problems
❓ MCQs
Just write the option 👍
Okay 🙂
Here is STILL MORE, continuing smoothly — deeper practice + exam traps + advanced Class 7 ICSE level, but still very easy language.
LINEAR EQUATIONS – EXTENDED NOTES (PART 13)
(Depth • Accuracy • 100% Exam Ready)
- WHAT MAKES A QUESTION “LINEAR”?
An equation is linear if:
Variable power is 1 only
No square (x²), cube (x³), root (√x)
✔ 3x + 5 = 14 → Linear
❌ x² + 2 = 5 → Not linear - IDENTIFY & SOLVE (EXAM TREND)
Question:
Which of the following are linear equations?
4x − 7 = 9 ✔
x² + 3 = 7 ❌
2(x + 5) = 20 ✔
√x + 2 = 6 ❌ - EQUATIONS WITH NEGATIVE NUMBERS
Example:
x − 5 = −3
x = −3 + 5
x = 2
Example:
−2x = 10
x = 10 ÷ (−2)
x = −5
👉 Always take care of signs! - BRACKETS ON BOTH SIDES
Example:
2(x + 3) = 3(x − 1)
2x + 6 = 3x − 3
2x − 3x = −3 − 6
−x = −9
x = 9 - FRACTIONS ON BOTH SIDES
Example:
x/2 + 1 = x/4 + 5
Multiply whole equation by 4:
2x + 4 = x + 20
2x − x = 20 − 4
x = 16 - DECIMAL TYPE QUESTIONS
Example:
0.5x = 10
x = 10 ÷ 0.5
x = 20
👉 Convert decimal to fraction if confused: 0.5 = 1/2 - “FIND THE NUMBER” QUESTIONS (VERY COMMON)
Question:
The sum of three consecutive numbers is 45. Find the numbers.
Let numbers be: x, x + 1, x + 2
Equation: x + (x + 1) + (x + 2) = 45
3x + 3 = 45
3x = 42
x = 14
Numbers: 14, 15, 16 - PERIMETER WORD PROBLEM
Question:
The perimeter of a square is 36 cm. Find the length of one side.
Let side = x
Perimeter = 4x
4x = 36
x = 9 cm - TIME TYPE WORD PROBLEM
Question:
Twice a number is 18 more than the number. Find the number.
Let number = x
2x = x + 18
x = 18 - THINK & SOLVE (HOTS)
Question:
If 5 is subtracted from three times a number, the result is 10.
Equation: 3x − 5 = 10
3x = 15
x = 5 - MATCH THE FOLLOWING (REVISION)
Equation
Value of x
x + 7 = 12
5
3x = 21
7
x/4 = 6
24
2x − 4 = 8
6 - WHY STUDENTS LOSE MARKS
❌ Skipping steps
❌ Wrong sign while transposing
❌ No statement for answer
❌ Untidy work
✔ ICSE prefers neat + logical presentation - MODEL ANSWER FORMAT (COPY THIS)
Let the number be x.
According to the question,
x + 5 = 17
Solving,
x = 12
Hence, the required number is 12. - SELF-CHECK QUESTIONS
Solve on your own:
x + 15 = 32
7x = 56
x/6 = 5
4x + 9 = 25
3(x − 2) = 15
(Answers: 17, 8, 30, 4, 7) - LAST-MINUTE EXAM TIPS
✔ Read question twice
✔ Form equation carefully
✔ Solve step by step
✔ Check once
✔ Underline final answer - ONE-LINE SUMMARY
Linear equations are easy when you stay calm and balance both sides. - YOU HAVE COMPLETED A FULL MEGA CHAPTER 🎉
This content is now:
Bigger than textbook
Enough for full marks
Suitable for revision + practice
If you still want MORE, choose ONE clearly:
1️⃣ Only 100 word problems
2️⃣ Only MCQs (ICSE pattern)
3️⃣ Sample paper (with marking scheme)
4️⃣ 2-page ultra-short notes
5️⃣ PDF printable notes
Just write the number 👍
Alright 👍
Here is EVEN MORE CONTINUATION, now focusing on EXAM DEPTH + TRICKY QUESTIONS + VERY HIGH PRACTICE, still Class 7 ICSE friendly and easy language.
LINEAR EQUATIONS – EXTENDED NOTES (PART 14)
(Tricky • Practice-Oriented • ICSE Exam Focus)
- TRICKY WORD STATEMENTS → SIMPLE EQUATIONS
Statement:
“Six less than a number is 10.”
❌ Wrong equation: 6 − x = 10
✔ Correct equation: x − 6 = 10
👉 Always locate “than” carefully. - “MORE THAN” vs “LESS THAN”
Sentence
Equation
5 more than x
x + 5
5 less than x
x − 5
x is 5 more than y
x = y + 5
x is 5 less than y
x = y − 5 - MIXED SIGN QUESTIONS
Example:
−3x + 7 = 1
−3x = 1 − 7
−3x = −6
x = 2 - FRACTION + BRACKET COMBINATION
Example:
(x + 4)/2 = 6
x + 4 = 12
x = 8 - WORD PROBLEMS ON CONSECUTIVE EVEN NUMBERS
Question:
The sum of two consecutive even numbers is 30. Find them.
Let numbers be: x, x + 2
Equation: x + (x + 2) = 30
2x + 2 = 30
2x = 28
x = 14
Numbers: 14, 16 - CONSECUTIVE ODD NUMBERS
Question:
The sum of three consecutive odd numbers is 45.
Let numbers: x, x + 2, x + 4
Equation: 3x + 6 = 45
3x = 39
x = 13
Numbers: 13, 15, 17 - MONEY DISTRIBUTION PROBLEM
Question:
A sum of ₹60 is divided between two persons such that one gets ₹10 more than the other. Find their shares.
Let smaller share = x
Larger share = x + 10
x + (x + 10) = 60
2x + 10 = 60
2x = 50
x = 25
Other share = ₹35 - LENGTH–BREADTH TYPE PROBLEM
Question:
The length of a rectangle is 5 cm more than its breadth. If breadth is 7 cm, find the length.
Length = 7 + 5 = 12 cm - THINKING QUESTION (VERY IMPORTANT)
Question:
If x + 4 = x + 6, is there a solution?
Simplify: 4 = 6 ❌ (False)
👉 No solution exists - SPECIAL CASE (EXAM AWARENESS)
Question:
Solve: 2x + 3 = 2x + 3
After simplifying: 0 = 0 ✔
👉 Infinitely many solutions - TRUE OR FALSE (FAST REVISION)
x² + 3 = 5 is linear ❌
5x = 15 is linear ✔
Linear equation has only one variable ✔
Power of variable is 1 ✔ - COMMON ICSE PRESENTATION MISTAKE
❌ Writing only answer
✔ Writing equation + steps + answer
Marks are given for method, not only answer. - SPEED PRACTICE (MENTAL MATH)
Solve quickly:
x − 8 = 4 → 12
9x = 81 → 9
x/10 = 3 → 30
2x + 6 = 14 → 4 - MIXED PRACTICE SET (IMPORTANT)
Solve:
1️⃣ x + 11 = 25
2️⃣ 4x − 5 = 19
3️⃣ x/8 = 7
4️⃣ 3(x + 2) = 21
5️⃣ 5x + 10 = 35
(Answers: 14, 6, 56, 5, 5) - MODEL WORD PROBLEM ANSWER (PERFECT FORMAT)
Let the required number be x.
According to the question,
x − 7 = 13
Solving,
x = 20
Hence, the required number is 20. - LAST 30-MINUTE REVISION STRATEGY
✔ Revise formulas
✔ Solve 10 easy questions
✔ Solve 5 word problems
✔ Check signs carefully - FINAL POWER STATEMENT
Linear equations is the easiest chapter to score full marks if practised well.
You now have PART 1 → PART 14, which is more than 5000+ words content.
If you still want MORE, please choose clearly (so I don’t repeat):
📝 100-word problems only
❓ MCQs with answers
📄 Printable PDF
🧠 HOTS / Olympiad type
📘 Ultra-short revision notes
📑 Sample paper (ICSE pattern)
Just write the option name 👍
Alright 👍
Here is MORE CONTINUATION, now focused on EXAM-LEVEL TRAPS + VERY HIGH PRACTICE + CONCEPT CLARITY, still Class 7 ICSE friendly and easy language.
LINEAR EQUATIONS – EXTENDED NOTES (PART 15)
(Exam Traps • Mastery • Perfection)
- EXAM TRAP: WRONG TRANSPOSITION
Question:
x + 9 = 3
❌ Wrong: x = 9 − 3
✔ Correct: x = 3 − 9
x = −6
👉 Always move numbers to the other side with sign change. - NEGATIVE ON BOTH SIDES
Example:
−x + 4 = −10
−x = −10 − 4
−x = −14
x = 14 - MULTIPLICATION & DIVISION TRAP
Example:
−4x = −20
x = −20 ÷ (−4)
x = 5
✔ Minus ÷ minus = plus - WORD PROBLEMS USING “TWICE” AND “THRICE”
Question:
Thrice a number is 27. Find the number.
3x = 27
x = 9
Question:
Twice a number decreased by 6 is 10.
2x − 6 = 10
2x = 16
x = 8 - “INCREASED BY” vs “DECREASED BY”
Phrase
Meaning
Increased by 7
+7
Decreased by 7
−7 - FRACTION WORD PROBLEMS
Question:
Half of a number is 15.
x/2 = 15
x = 30
Question:
One-fourth of a number is 9.
x/4 = 9
x = 36 - MIXED WORD PROBLEM (ICSE STYLE)
Question:
The sum of a number and its half is 18. Find the number.
Let number = x
x + x/2 = 18
Multiply by 2:
2x + x = 36
3x = 36
x = 12 - AGE PROBLEM (SLIGHTLY TRICKY)
Question:
Five years ago, Ravi’s age was thrice his son’s age. Ravi is now 35 years old. Find his son’s present age.
Let son’s present age = x
Five years ago: Son = x − 5
Ravi = 35 − 5 = 30
Equation: 30 = 3(x − 5)
30 = 3x − 15
3x = 45
x = 15 years - CHECKING WORD PROBLEM ANSWERS
Always:
Substitute value
Read sentence again
Confirm logic - CASE STUDY TYPE QUESTIONS (NEW TREND)
Situation:
A number when multiplied by 4 and reduced by 8 gives 20.
Equation: 4x − 8 = 20
4x = 28
x = 7 - ASSERTION–REASON TYPE
Assertion: x + 5 = 12 has one solution
Reason: Linear equations have only one solution
✔ Both are true - VERY SHORT ANSWER (1 MARK)
Degree of linear equation → 1
Number of solutions → One
Example → 2x + 3 = 7 - FILL IN THE BLANKS
Linear equation has power of variable equal to _ → 1 x + 7 = 10 has solution _ → 3 - MATCH THE COLUMNS
Column A
Column B
x + 6 = 14
8
5x = 40
8
x/3 = 4
12
2x − 4 = 6
5 - WHY PRACTICE MATTERS MOST HERE
Because:
Same pattern repeats
Only numbers change
Logic remains same - GOLDEN EXAM RULE
Equation first, answer last. - SPEED ROUND (30 SECONDS)
x − 11 = 9 → 20
6x = 54 → 9
x/9 = 5 → 45
7x + 7 = 21 → 2 - FINAL PRACTICE SET
Solve:
1️⃣ x + 18 = 40
2️⃣ 9x = 72
3️⃣ x/12 = 4
4️⃣ 2(x − 3) = 10
5️⃣ 5x − 15 = 10
(Answers: 22, 8, 48, 8, 5) - FINAL CONFIDENCE BOOST
You have now: ✔ Concept
✔ Practice
✔ Tricky questions
✔ Word problems
✔ Exam pattern
This chapter is now FULLY MASTERED.
If you still want MORE, tell me exactly what type, for example:
“Only age problems”
“Only case study questions”
“Only MCQs (50)”
“One full test paper”
“Ultra-short revision notes”
Just write it 👍
Got it 🙂
Here is MORE CONTINUATION, but now in a NEW STYLE so it doesn’t feel repetitive.
This part focuses on DEEP UNDERSTANDING + STEP-BY-STEP THINKING + CONFIDENCE BUILDING for Class 7 ICSE Linear Equations.
LINEAR EQUATIONS – EXTENDED NOTES (PART 16)
(Concept Strength • Thinking Skill • Zero Fear)
- THINK BEFORE SOLVING (MOST IMPORTANT HABIT)
Before writing anything, ask:
What is given?
What is required?
Which number is unknown?
This saves mistakes. - TRANSLATING ENGLISH → MATH (CORE SKILL)
Sentence:
“The sum of a number and 9 is equal to 25.”
👉 Break it:
“Sum of” → +
“A number” → x
“Is equal to” → =
Equation: x + 9 = 25 - DIRECTION WORDS (VERY IMPORTANT)
Sentence
Correct Meaning
7 less than a number
x − 7
A number less than 7
7 − x
5 more than twice a number
2x + 5
Twice the sum of a number and 3
2(x + 3) - WHY BRACKETS CHANGE EVERYTHING
Compare:
1️⃣ 2x + 3
2️⃣ 2(x + 3)
If x = 4:
2x + 3 = 8 + 3 = 11
2(x + 3) = 2 × 7 = 14
👉 Brackets are very powerful. - DISTRIBUTIVE LAW REVISION
a(b + c) = ab + ac
Examples:
3(x + 2) = 3x + 6
5(2x − 1) = 10x − 5 - MULTI-STEP EQUATION (DON’T PANIC)
Question:
3(x − 2) + 5 = 2x + 9
Step 1: Open brackets
3x − 6 + 5 = 2x + 9
Step 2: Simplify
3x − 1 = 2x + 9
Step 3: Solve
x = 10 - WHY WE “TRANSPOSE” TERMS
To keep equation balanced.
Example: x + 6 = 14
Instead of thinking “move 6”, think: “What should I do to remove +6?”
👉 Subtract 6 from both sides - CHECKING IS NOT OPTIONAL
Example:
x = 10
Original equation: x + 6 = 14
Check: 10 + 6 = 16 ❌
👉 Answer is wrong
Checking saves marks! - COMMON STUDENT CONFUSION CLEARED
❓ Can x be negative?
✔ Yes
❓ Can answer be a fraction?
✔ Yes
❓ Can equation have no solution?
✔ Yes (rare, but possible) - SPECIAL TYPE: NO SOLUTION
Example: x + 5 = x + 7
Subtract x from both sides: 5 = 7 ❌
👉 No solution - SPECIAL TYPE: INFINITE SOLUTIONS
Example: 2x + 3 = 2x + 3
After simplifying: 0 = 0 ✔
👉 Infinite solutions - STORY-BASED QUESTION (ICSE STYLE)
Question:
A number when added to its double becomes 27. Find the number.
Let number = x
x + 2x = 27
3x = 27
x = 9 - STEP FORMAT THAT SCORES FULL MARKS
Always write like this:
Let the number be x.
According to the question,
x + 2x = 27
Solving,
x = 9
Hence, the required number is 9. - SELF-PRACTICE (VERY IMPORTANT)
Solve on your own:
1️⃣ x + 13 = 40
2️⃣ 8x = 64
3️⃣ x/7 = 6
4️⃣ 5(x − 1) = 20
5️⃣ x + x/2 = 18
(Answers: 27, 8, 42, 5, 12) - WHY LINEAR EQUATIONS ARE SCORING
Because:
No formulas to remember
Steps are fixed
Logic is simple
Practice = perfection - FINAL GOLDEN LINE
Linear equations reward patience, not speed.
You now have PART 1 → PART 16, which is far more than any guidebook.
👉 If you want MORE, please specify ONE clearly so I can give new content:
📘 Only word problems (50/100)
❓ Only MCQs
📝 Full ICSE test paper
📄 PDF printable notes
✂️ Ultra-short revision notes
Just write the option 😊
Alright 🙂
Here is MORE CONTINUATION, but now this will be FINAL-LEVEL DEPTH, covering EVERY POSSIBLE ICSE ANGLE so that nothing remains uncovered.
This part focuses on thinking questions, exam psychology, mixed practice, and mastery.
LINEAR EQUATIONS – EXTENDED NOTES (PART 17)
(Mastery • Confidence • 100% Coverage)
- HOW EXAMINERS FRAME QUESTIONS
ICSE examiners usually test:
Understanding of language
Correct equation formation
Neat stepwise solving
Logical checking
👉 They do not try to confuse, but they test carelessness. - IDENTIFY THE UNKNOWN CORRECTLY
Wrong start = wrong answer.
Example sentence:
“The difference between a number and 9 is 14.”
Correct thinking:
“Difference between” → subtraction
Number comes first
Equation: x − 9 = 14
✔ Not 9 − x - REVERSE LANGUAGE TRAP
Sentence: “Seven is subtracted from a number.”
Correct equation: x − 7
❌ Not 7 − x - MORE TRANSLATION PRACTICE
Convert to equations:
1️⃣ A number increased by 12 is 40
→ x + 12 = 40
2️⃣ Five times a number is 60
→ 5x = 60
3️⃣ The quotient of a number and 4 is 6
→ x/4 = 6 - MULTI-OPERATION WORD PROBLEM
Question:
Three times a number increased by 5 is equal to 26.
Correct equation: 3x + 5 = 26
Solving: 3x = 21
x = 7 - WHY STUDENTS PANIC (AND HOW NOT TO)
Students panic because: ❌ Long sentences
❌ Big numbers
❌ Many words
Solution: ✔ Ignore extra words
✔ Find key math words
✔ Convert calmly - MIXED SIGN PRACTICE
Solve:
1️⃣ x − 14 = −6 → 8
2️⃣ −5x = 25 → −5
3️⃣ −x + 3 = 11 → −8 - DECIMAL WORD PROBLEM
Question:
Half of a number increased by 2.5 is 12.5.
Equation: x/2 + 2.5 = 12.5
x/2 = 10
x = 20 - WHY FRACTIONS SHOULD BE CLEARED EARLY
Example: x/3 + x/6 = 10
LCM = 6
Multiply whole equation by 6:
2x + x = 60
3x = 60
x = 20 - COMPARISON TYPE QUESTIONS
Question:
Twice a number is equal to the number increased by 14.
Equation: 2x = x + 14
x = 14 - EXAM TRAP: EXTRA INFORMATION
Question:
A boy thinks of a number. The number is positive. If the number is multiplied by 4 and 8 is subtracted, the result is 20. Find the number.
👉 “Positive” is extra information.
Equation: 4x − 8 = 20
x = 7 - STEP-MARKS SECRET (VERY IMPORTANT)
Even if final answer is wrong: ✔ Correct equation → marks
✔ Correct steps → marks
Never leave solution incomplete. - HOTS (HIGH ORDER THINKING SKILL)
Question:
If x + 5 = 15 − x, find x.
x + x = 15 − 5
2x = 10
x = 5 - ASSERTION-REASON PRACTICE
Assertion: 3x = 12 has solution x = 4
Reason: Linear equations have exactly one solution
✔ Both true ✔ Reason explains assertion - VERY SHORT ANSWERS (REVISION)
1️⃣ Degree of linear equation → 1
2️⃣ Max power of variable → 1
3️⃣ Example → x + 3 = 7 - ERROR SPOTTING PRACTICE
Student wrote: x − 4 = 10
x = 4 − 10
Mistake: 👉 Sign changed wrongly
Correct: x = 10 + 4 = 14 - COMPLETE PRACTICE SET (MIXED)
Solve:
1️⃣ x + 22 = 50
2️⃣ 6x = 66
3️⃣ x/11 = 3
4️⃣ 4(x − 2) = 24
5️⃣ x + x/3 = 16
(Answers: 28, 11, 33, 8, 12) - LAST-DAY EXAM STRATEGY
✔ Start with easy questions
✔ Keep handwriting neat
✔ Don’t skip steps
✔ Check signs once
✔ Underline final answer - FINAL MOTIVATION LINE
If you understand language, linear equations become automatic.
🎉 YOU HAVE NOW COMPLETED
PART 1 → PART 17
This is more than 6000+ words, enough for:
Full marks
Teaching others
Strong foundation for higher classes
If you want ANYTHING ELSE, please be specific so I don’t repeat:
📄 PDF printable notes
📝 One full ICSE sample paper
❓ Only MCQs (50/100)
✂️ 2-page ultra-short notes
🧠 Olympiad-level questions
Just write what you want 👍
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