How many practice questions are available for Linear Equations?

SparkEd Math offers 60+ practice questions for Linear Equations across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Linear Equations content free on SparkEd Math?

Yes! All Linear Equations content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Linear Equations differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Linear Equations problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Linear Equations content aligned with the ICSE syllabus?

Yes, all Linear Equations questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Linear Equations — Class 7 ICSE (2025-26)

About Linear Equations — Class 7 ICSE

Solve simple linear equations in one variable and apply them to word problems. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 6). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Linear Equations

Introduction to Linear Equations: What, Why, and How
Solving Simple Linear Equations: The Transposition Method
Solving Equations with Multiplication and Division
Multi-Step Equations and Introduction to Word Problems
Summary, Verification, and Framing Word Problems

Interactive lesson · about 15 minutes · checkpoint question after every unit

Linear Equations — solved examples for Class 7 ICSE

Example 1easy

Which of the following statements correctly describes a linear equation in one variable?

A)It is an expression with an equals sign.
B)It is an equation where the highest power of the variable is 1.
C)It is an equation that always has two variables.
D)It is a mathematical statement that compares two unequal values.

Step-by-step solution

A linear equation in one variable involves only one unknown quantity.
The term 'linear' means that when graphed, it forms a straight line, which implies the highest power of the variable is 1.
An expression does not have an equals sign, and an equation compares two equal values.

Answer: It is an equation where the highest power of the variable is 1.

Example 2medium

Which of the following is a linear equation in one variable?

A)2x + 5y = 7
B)x² - 3 = 6
C)4p - 9 = 15
D)y + 2 > 10

Step-by-step solution

Option A, '2x + 5y = 7', has two variables (x and y), so it is not an equation in one variable.
Option B, 'x² - 3 = 6', has the variable x raised to the power of 2, so it is not a linear equation.
Option C, '4p - 9 = 15', has only one variable (p) raised to the power of 1, and an equality sign. This fits the definition of a linear equation in one variable.
Option D, 'y + 2 > 10', is an inequality, not an equation, because it uses the '>' sign instead of '='.

Answer: 4p - 9 = 15

Example 3hard

The sum of three consecutive multiples of 4 is 12 more than five times the smallest multiple. What is the largest of these multiples?

A)4
B)8
C)12
D)16

Step-by-step solution

Let the smallest multiple of 4 be 'x'. Then the next two consecutive multiples are 'x + 4' and 'x + 8'.
The sum of these three multiples is x + (x + 4) + (x + 8) = 3x + 12.
According to the problem, this sum is 12 more than five times the smallest multiple: 3x + 12 = 5x + 12.
Solving the equation: 3x + 12 = 5x + 12 => 2x = 0 => x = 0. The multiples are 0, 4, 8. The largest multiple is 8.

Answer: 8

Practice questions on Linear Equations

Q1.easy
Rohan was solving the equation x + 7 = 15. He wrote his steps as: x = 15 + 7. Which of the following statements about Rohan's solution is true?
1. A)Rohan correctly applied the property of equality.
2. B)Rohan made a mistake by adding 7 to 15 instead of subtracting it.
3. C)Rohan made a mistake by transposing +7 as +7 to the other side.
4. D)Rohan should have divided 15 by 7.
Show answer
Answer: Rohan made a mistake by transposing +7 as +7 to the other side.
Hint: When you move a term from one side of the equation to the other, what happens to its sign?
Q2.easy
The sum of a number and 12 is 30. Which of the following equations represents this statement?
1. A)n + 12 = 30
2. B)12n = 30
3. C)n - 12 = 30
4. D)n / 12 = 30
Show answer
Answer: n + 12 = 30
Hint: 'Sum' means addition, and 'a number' can be represented by a variable.
Q3.easy
Solve the equation: 3x - 5 = 10
1. A)x = 3
2. B)x = 4
3. C)x = 15
4. D)x = 5
Show answer
Answer: x = 5
Hint: First, move the constant term to the right side, then deal with the coefficient of x.
Q4.medium
If you subtract 7 from three times a number, you get 14. Which equation represents this statement?
1. A)3x - 7 = 14
2. B)7 - 3x = 14
3. C)3(x - 7) = 14
4. D)7x - 3 = 14
Show answer
Answer: 3x - 7 = 14
Hint: Let the unknown number be 'x'. 'Three times a number' means 3x. 'Subtract 7 from' means 7 is taken away from that quantity.
Q5.medium
Solve the equation: p + 12 = 25
1. A)p = 13
2. B)p = 37
3. C)p = 25
4. D)p = 12
Show answer
Answer: p = 13
Hint: To isolate 'p', you need to perform the inverse operation of addition on both sides of the equation.
Q6.medium
Find the value of x in the equation: 4x = 36
1. A)x = 9
2. B)x = 32
3. C)x = 40
4. D)x = 144
Show answer
Answer: x = 9
Hint: The operation between 4 and x is multiplication. To solve for x, you need to perform the inverse operation.
Q7.hard
When a number is doubled and then 7 is subtracted, the result is the same as when the number is increased by 5 and then the entire quantity is multiplied by 3/2. What is the number?
1. A)23
2. B)29
3. C)31
4. D)35
Show answer
Answer: 29
Hint: Translate each part of the word problem into an algebraic expression and equate them to form a linear equation. Pay close attention to the order of operations.
Q8.hard
Rohan solved the equation `5x - (2x - 3) = 18` as follows:
Step 1: `5x - 2x - 3 = 18`
Step 2: `3x - 3 = 18`
Step 3: `3x = 21`
Step 4: `x = 7`
Which step contains the first mistake in Rohan's solution?
1. A)Step 1
2. B)Step 2
3. C)Step 3
4. D)Step 4
Show answer
Answer: Step 1
Hint: When removing brackets preceded by a minus sign, remember to change the sign of every term inside the bracket.
Q9.hard
In a triangle, the second angle is twice the first angle, and the third angle is 30° more than the second angle. Find the measure of the smallest angle.
1. A)30°
2. B)60°
3. C)90°
4. D)120°
Show answer
Answer: 30°
Hint: Recall the fundamental property of the sum of angles in a triangle. Represent each angle in terms of a single variable.

These are 9 of the 60 questions available for Linear Equations. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.