How many practice questions are available for Linear Equations in One Variable?

SparkEd Math offers 60+ practice questions for Linear Equations in One Variable 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 in One Variable content free on SparkEd Math?

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How does SparkEd Math teach Linear Equations in One Variable differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Linear Equations in One Variable 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 in One Variable content aligned with the ICSE syllabus?

Yes, all Linear Equations in One Variable questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 8. The content follows the official curriculum structure and exam pattern.

Linear Equations in One Variable — Class 8 ICSE (2025-26)

About Linear Equations in One Variable — Class 8 ICSE

Solve linear equations with variables on both sides and apply to practical problems. This topic is part of the ICSE Class 8 mathematics syllabus (chapter: Chapter 7). 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 in One Variable

Introduction to Linear Equations
Solving Equations Using Transposition
Equations with Variables on Both Sides
Applications: Solving Word Problems
Summary, Advanced Cases, and Practice

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

Linear Equations in One Variable — solved examples for Class 8 ICSE

Example 1easy

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

A)A) It is an equation where the highest power of the variable is 2.
B)B) It is an equation that always has two different variables.
C)C) It is an equation where the highest power of the single variable is 1.
D)D) It is an inequality statement involving one variable.

Step-by-step solution

A linear equation has a variable with the highest power of 1. If the highest power were 2, it would be a quadratic equation.
'One variable' means only one type of unknown (e.g., only 'x' or only 'y') is present in the equation.
Therefore, option C correctly defines a linear equation in one variable.
$ax + b = 0, where a ≠ 0$

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

Example 2medium

Solve for x: 5(2x - 3) - 3(x + 2) = 4(2x - 1) + 5

A)x = -20
B)x = -10
C)x = 10
D)x = 20

Step-by-step solution

Expand the brackets: 10x - 15 - 3x - 6 = 8x - 4 + 5
Combine like terms on each side: 7x - 21 = 8x + 1
Move 'x' terms to one side and constants to the other: 7x - 8x = 1 + 21
Simplify and solve for x: -x = 22, so x = -22.

Answer: x = -20

Example 3hard

Solve for x: (2/3) [ (x/2) + (3/4)(x - 1) ] = 7/6

Step-by-step solution

First, simplify inside the square brackets: (x/2) + (3/4)(x - 1) = x/2 + (3x - 3)/4.
Find a common denominator for the terms inside the bracket: (2x/4) + (3x - 3)/4 = (2x + 3x - 3)/4 = (5x - 3)/4.
Substitute back into the original equation: (2/3) * (5x - 3)/4 = 7/6.
Multiply both sides by 3/2 to isolate (5x - 3)/4: (5x - 3)/4 = (7/6) * (3/2) = 7/4.
Multiply both sides by 4: 5x - 3 = 7.
Add 3 to both sides: 5x = 10.
Divide by 5: x = 2.

Answer: 2

Practice questions on Linear Equations in One Variable

Q1.easy
Ravi was solving the equation 3x - 5 = 10. He wrote the next step as 3x = 10 - 5. What mistake did he make?
1. A)A) He should have divided 3x by 3 first.
2. B)B) When -5 is transposed to the other side, it should become +5.
3. C)C) He should have subtracted 10 from 5.
4. D)D) There is no mistake; his step is correct.
Show answer
Answer: B) When -5 is transposed to the other side, it should become +5.
Hint: Recall the rule for transposing terms from one side of an equation to the other.
Q2.easy
Solve for x: 5x - 5 = 2x + 13
1. A)A) x = 2
2. B)B) x = 4
3. C)C) x = 5
4. D)D) x = 6
Show answer
Answer: D) x = 6
Hint: Gather all variable terms on one side and constant terms on the other side.
Q3.easy
A number when multiplied by 4 and then decreased by 7 gives 13. Which of the following equations represents this statement?
1. A)A) 4x - 7 = 13
2. B)B) 7x - 4 = 13
3. C)C) 4(x - 7) = 13
4. D)D) x/4 - 7 = 13
Show answer
Answer: A) 4x - 7 = 13
Hint: Let the unknown number be 'x'. Translate 'multiplied by 4' and 'decreased by 7' in that sequence.
Q4.medium
Three consecutive multiples of 7 sum to 315. Find the largest of these three multiples.
1. A)98
2. B)105
3. C)112
4. D)119
Show answer
Answer: 112
Hint: Let the first multiple of 7 be 7x. How would you represent the next two consecutive multiples of 7?
Q5.medium
A father's current age is 3 times his son's current age. In 10 years, the father's age will be twice his son's age. What is the son's current age?
1. A)10 years
2. B)12 years
3. C)15 years
4. D)20 years
Show answer
Answer: 10 years
Hint: Let the son's current age be 'x'. Express the father's current age and their ages in 10 years in terms of 'x'.
Q6.medium
Solve for y: (y + 6)/4 - (y - 3)/5 = (5y - 4)/8
1. A)y = 4
2. B)y = 8
3. C)y = 12
4. D)y = 16
Show answer
Answer: y = 4
Hint: Find the Least Common Multiple (LCM) of the denominators (4, 5, 8) to clear the fractions. Multiply every term by the LCM.
Q7.hard
The sum of three consecutive multiples of 7 is 357. What is the sum of the smallest and largest of these multiples?
1. A)238
2. B)245
3. C)252
4. D)266
Show answer
Answer: 238
Hint: Represent the three consecutive multiples of 7 using a single variable. For example, if the first multiple is 7x, what would be the next two?
Q8.hard
If x = -3 is the solution to the equation (a/2)(x - 1) + (a/3)(x - 2) = 11, find the value of 'a'.
1. A)6
2. B)-6
3. C)3
4. D)-3
Show answer
Answer: -3
Hint: Substitute the given value of x into the equation first. Then, simplify the expression to solve for 'a'.
Q9.hard
Consider the equation (k - 2)x + 5 = 3x + 7. For what value of 'k' will this equation have no unique solution for x?
1. A)2
2. B)3
3. C)5
4. D)7
Show answer
Answer: 5
Hint: An equation has no unique solution (either no solution or infinitely many solutions) when the coefficients of the variable on both sides are equal. Consider what happens to the constants in such a case.

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