Linear equations

An equation is a balance: whatever you do to one side, do to the other. Undo each step until x is on its own.

Key facts

  • Do the same thing to both sides.
  • Undo + and − first, then × and ÷.
  • Check by putting your answer back in.

Worked examples

Example 1

Solve 3x + 5 = 20.

  1. Take 5 from both sides. 3x = 15
  2. Divide both sides by 3. x = 5
  3. Check: 3 × 5 + 5 = 20 ✓

Answer: x = 5

Example 2

Solve 5x − 4 = 2x + 11.

  1. Take 2x from both sides. 3x − 4 = 11
  2. Add 4 to both sides. 3x = 15
  3. Divide by 3. x = 5

Answer: x = 5

Questions about linear equations