Multi-step equations | Year 8

01 / LEARN

The idea, step by step

What solving means

A solution makes the original statement true. An equation is balanced, so adding, subtracting, multiplying or dividing must be applied to both sides. Division is permitted only by a non-zero number.

Collect like terms on one side first. Then undo addition or subtraction outside the unknown term, before undoing its multiplication or division.

Show equivalent statements

Write one balanced change per line so another person can follow your argument. Do not round a fraction just because you expected a whole-number answer.

Finish by substituting into the original equation. This checks the result without repeating the same rearrangement.

A common trap

Changing a term sign without a balanced operation.

Instead: State what you do to both sides; subtracting 7 explains why a +7 disappears.

02 / WORKED EXAMPLES

See the thinking

Example 1

Undo two operations

Solve $4 x + 7 = 31$ .

Subtract 7: $4 x = 24$ .
Divide by 4: $x = 6$ .
Check $4 (6) + 7 = 31$ .

x = 6

Example 2

Collect terms first

Solve $5 x + 8 - 2 x = 20$ .

Combine the x terms: $3 x + 8 = 20$ .
Subtract 8, then divide by 3.
Check $5 (4) + 8 - 2 (4) = 20$ .

x = 4

Check your understanding

Solve $3 x - 5 = 16$ .

Show answer

$x = 7$ .

Add 5 to get $3 x = 21$ , then divide by 3.

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Solve $2 x + 5 = 17$ .
2 marks
Solve $5 x - 4 = 26$ .
2 marks
Solve $7 + 3 x = 1$ .
2 marks
Solve $6 x + 4 - 2 x = 24$ .
2 marks
Solve $x / 3 + 4 = 9$ .
2 marks
Bike hire costs AUD 6 plus AUD 4 per hour. The bill is AUD 26. Write and solve an equation for the hours.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Solve $2 x + 5 = 17$ .
2 marks
Subtract 5 to get $2 x = 12$ .
Divide by 2; check $12 + 5 = 17$ .
$x = 6$ .
Solve $5 x - 4 = 26$ .
2 marks
Add 4 to get $5 x = 30$ .
Divide by 5.
$x = 6$ .
Solve $7 + 3 x = 1$ .
2 marks
Subtract 7 to get $3 x = - 6$ .
Divide by 3 and check.
$x = - 2$ .
Solve $6 x + 4 - 2 x = 24$ .
2 marks
Collect terms: $4 x + 4 = 24$ .
Subtract 4 and divide by 4.
$x = 5$ .
Solve $x / 3 + 4 = 9$ .
2 marks
Subtract 4: $x / 3 = 5$ .
Multiply by 3.
$x = 15$ .
Bike hire costs AUD 6 plus AUD 4 per hour. The bill is AUD 26. Write and solve an equation for the hours.
3 marks
Remove the fixed charge: $4 h = 20$ .
Divide by 4 and check $6 + 4 (5) = 26$ .
$6 + 4 h = 26$ ; 5 hours.

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Brackets and variables on both sides

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics (2026)

Multi-step equations; brackets and variables on both sides; equations with rational solutions; substitution checks; one-variable inequalities and number-line solutions; tables and straight-line graphs; horizontal/vertical lines; how coefficients change a graph; graphical solutions and intersection checks; real-world linear models with digital exploration.

Official curriculum source ↗

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