R
Rishtaara
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.

  1. 13x − 2x = 12 − 5
  2. 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.

  1. 1Let son = x, father = x+30
  2. 2x + x + 30 = 56
  3. 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: