Solving linear equations: Year 8 introduction

Understand the key idea

Keep an equation balanced by adding or subtracting the same amount on both sides, or multiplying or dividing both sides by the same non-zero number. Choose inverse steps that match the equation: for 3x + 4 = 19, subtract 4, then divide by 3 to get x = 5. For (x + 3) ÷ 2 = 5, multiply both sides by 2, then subtract 3 to get x = 7. Check by substituting your answer into the original equation.

Common mix-up

Apply each operation to the whole of both sides. For 2x + 3 = 11, subtracting 3 gives 2x = 11 − 3 = 8, then dividing both sides by 2 gives x = 4. Writing 2x = 11 would leave the right-hand side unchanged and break the balance.

Try this first

1. Solve 3x + 4 = 19 and check the answer by substitution.
2. Solve an equation where the unknown appears on both sides.
3. Write an equation for "I think of a number, double it and add 5 to get 17".

Ask: How can you check an equation answer is right without asking anyone?