MathsIntermediateYear 7–9 · Ages 11–14

KS3 Maths: Solving Linear Equations

A KS3 algebra worksheet covering solving one-step and two-step linear equations, equations with unknowns on both sides, and forming equations from word problems.

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Learning objectives

Solve one-step and two-step linear equations
Solve equations with the unknown on both sides
Form and solve equations from written descriptions

Instructions

Solve each equation, showing all steps. Check your answers by substituting back into the original equation.

Questions

Solve: x + 9 = 17

Solve: 3y = 27

Solve: 2x + 5 = 13

Solve: 4n − 3 = 21

Solve: 3x + 2 = x + 10

Solve: 5a − 4 = 2a + 8

Solve: 7 − 2x = 1

Solve: (x + 3)/2 = 5

I think of a number, multiply it by 4, then subtract 6. The result is 18. Write and solve an equation to find the number.

The perimeter of a rectangle is 34 cm. The length is x cm and the width is (x − 3) cm. Form and solve an equation to find x.

Solve: 3(x + 4) = 21

Solve: 2(3x − 1) = 4x + 6

Answer Key

Teacher / Parent copy

1.x = 8

2.y = 9

3.x = 4

4.n = 6

5.x = 4

6.a = 4

7.x = 3

8.x = 7

9.4n − 6 = 18 → 4n = 24 → n = 6

10.2(x + x − 3) = 34 → 2(2x − 3) = 34 → 4x − 6 = 34 → 4x = 40 → x = 10. Length = 10 cm, width = 7 cm.

11.x = 3 (expand: 3x + 12 = 21, 3x = 9, x = 3)

12.x = 4 (6x − 2 = 4x + 6, 2x = 8, x = 4)

Teacher note

Encourage pupils to always check their answers by substituting back. A common misconception is changing signs incorrectly when moving terms across the equals sign — address this explicitly. Questions 11–12 introduce expanding brackets, linking algebra to earlier skills.

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