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Auralith Learning

Year 8 · Maths · Brackets and equations · Lesson 3

Harder equations

Learn to solve equations with brackets and with the unknown on both sides, and to form and solve them from number puzzles, shapes and angles.

Whiteboard video lesson: Harder equations

36-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Solve equations with brackets by expanding first
  • Solve equations with the unknown on both sides
  • Solve equations with negative solutions
  • Form equations from puzzles, shapes and angles
  • Check solutions in the original equation

The method

  1. Expand any brackets.
  2. If x is on both sides, subtract the smaller x term from both sides.
  3. Undo + or −, then × or ÷.
  4. Check in the original equation.

Key words: equation, expand, unknown, both sides, solve.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Solve 3(x + 2) = 21.

  1. Step 1: 3(x + 2) = 3x + 6
  2. Step 2: Subtract 6 both sides
  3. Step 3: Divide by 3
  4. Step 4: Write x = ...
  5. Step 5: Check: left = 21, right = 21

Answer: x = 5

Question 2

Solve 4(x − 3) = 20.

  1. Step 1: 4(x − 3) = 4x − 12
  2. Step 2: Add 12 both sides
  3. Step 3: Divide by 4
  4. Step 4: Write x = ...
  5. Step 5: Check: left = 20, right = 20

Answer: x = 8

Question 3

Solve 2(3x + 1) = 26.

  1. Step 1: 2(3x + 1) = 6x + 2
  2. Step 2: Subtract 2 both sides
  3. Step 3: Divide by 6
  4. Step 4: Write x = ...
  5. Step 5: Check: left = 26, right = 26

Answer: x = 4