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Year 8 Maths | Understand, justify, check

Solve an equation by preserving equality

An equation states that two expressions have equal value. Solving means finding a value that makes that statement true. Each step should preserve equality rather than move symbols according to an unexplained rule.

What to notice

The operations act in an order. In 3x + 4, multiplication happens before addition. To isolate x, undo the addition before undoing multiplication.

What to do

Apply the same operation to both sides, write the simpler equation and continue until x is isolated. Substitute the result into the original equation, including any brackets.

Why it works

Doing the same thing to equal quantities keeps them equal. Substitution provides an independent check and can reveal a mistake that a tidy-looking sequence of steps hides.

Work through an example

Solve 4x + 3 = 27.

  1. Subtract 3 from both sides: 4x = 24.
  2. Divide both sides by 4: x = 6.
  3. Check: 4 × 6 + 3 = 27. The original equation is true.

A common mistake

In 3(x + 4), the 3 multiplies both terms. Expanding gives 3x + 12, not 3x + 4. Alternatively, divide both sides by 3 before opening the brackets.

A strategy to try

Explain each line with an operation applied to both sides. If you cannot name the operation, pause before relying on the next line.

Try it now

Try three questions

No account is needed. These examples do not change saved learning progress. Choose an answer and check it for an explanation; you can try again.

1. Solve 5x − 7 = 18.
Help: a starting point

Identify the operation performed after multiplying x by 5.

Help: the next step

Undo subtracting 7 on both sides before dividing by 5.

2. Solve 3(x + 4) = 30.
Help: a starting point

Consider dividing both sides by the multiplier outside the brackets.

Help: the next step

Once x + 4 is isolated, undo the addition on both sides.

3. Solve 4x + 2 = 2x + 16.
Help: a starting point

Collect the x terms on one side by subtracting 2x from both sides.

Help: the next step

Then remove the remaining constant and divide by the remaining coefficient.

For parents and carers

Ask for a substitution check rather than judging only the final value. The examples move from two-step equations to brackets and an unknown on both sides. They sample the method without claiming to cover every type of algebraic equation.

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