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MathidiaMathematics Academy
Equations and inequalities
Lesson 21 of 75
Introduction

Equations with brackets

Objective. Solve linear equations involving a bracket.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Equations with brackets require expanding the bracket first so the equation becomes a standard linear form that can be solved by balancing both sides. For an equation like 3(x + 2) = 18, expand to get 3x + 6 = 18, then subtract 6 from both sides to get 3x = 12, and divide by 3 to find x = 4. Expanding before solving avoids errors that occur when trying to divide only part of an equation by the number outside the bracket. Always check the solution by substituting it back into the original unexpanded equation.

Worked example

Solve the equation with brackets 5(x − 3) = 20.

5 … 3
Illustrated card showing 5 … 3
  1. 1Expand the bracket: 5x − 15 = 20
  2. 2Add 15 to both sides: 5x = 35
  3. 3Divide both sides by 5: x = 7
  4. 4Check: 5(7 − 3) = 5 × 4 = 20

Answer: x = 7

Concept mastery

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Practice

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Common mistake. Pupils sometimes divide only the right-hand side by the number outside the bracket, turning 3(x + 2) = 18 into x + 2 = 6 which is actually correct, but often they instead subtract 2 before dividing, getting 3x = 16 incorrectly instead of expanding fully first.

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