Mathematics · Class 8
Linear Equations in One Variable
Reducing equations, variables on both sides, and applications.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Linear equations in one variable have highest power 1. Solve equations with variables on both sides, brackets, and applications to numbers, perimeters, and ages.
Solving Steps
- Simplify both sides (expand brackets)
- Transpose variable terms to one side, constants to other
- Divide by coefficient of variable
Equations with Fractions
Multiply both sides by LCM of denominators to clear fractions before solving.
Applications
- Consecutive integers, age problems
- Perimeter equations for rectangles
- Coins and two-digit number puzzles
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Variables Both Sides
Solve 3x + 5 = 2x + 12.
- 13x − 2x = 12 − 5
- 2x = 7
Answer
x = 7
Example 2: Age Problem
Father is 30 years older than son. Sum of ages is 56. Find son's age.
- 1Let son = x, father = x+30
- 2x + x + 30 = 56
- 32x = 26
Answer
Son is 13 years old
Key Points to Remember
- ✓ Linear equation: degree 1 in variable
- ✓ Unique solution for ax+b=0 when a≠0
- ✓ Always verify solution
Exam Tips
- • Show balancing each step
- • Define variables with units in word problems
Practice MCQs — Linear Equations in One Variable
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Solution of 5x − 3 = 2x + 9: