Maths Library

Two-step and multi-step equations: Year 8 maths

This topic covers solving equations requiring two or more algebraic steps, including brackets and unknowns on both sides. The worksheet guides pupils through inverse operations systematically to isolate the variable.

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What this covers

Two-step and multi-step equations is taught in Year 8 (age 12 to 13, KS3) as a main teaching focus. It sits in the Algebra strand.

Worked example

Solve: 4x - 7 = 2x + 9

  1. Subtract 2x from both sides: 2x - 7 = 9
  2. Add 7 to both sides: 2x = 16
  3. Divide both sides by 2: x = 8

Answer: x = 8

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Two-step equations of the form ax + b = c with positive integers
  2. Two-step equations involving negative integers or divisions, e.g., x/3 - 4 = 5
  3. Equations with brackets, e.g., 3(2x - 1) = 21
  4. Equations with the unknown on both sides, e.g., 5x + 2 = 2x + 14
  5. Multi-step equations with brackets and unknowns on both sides, e.g., 3(x + 2) = 5x - 8

Common mistakes

  • Dividing before eliminating the constant term, leading to fraction arithmetic errors
  • Failing to change signs correctly when moving terms across the equals sign

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Solve two-step and multi-step linear equations with integer coefficients.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Two-step and multi-step equations

Year 8 maths

Qs
6
Marks
18
NameDateScore / 18
1.
6x + 10 = -2
[3]
2.
3x + 10 = 31
[3]
3.
3x + 4 = 16
[3]
4.
3x + 11 = 38
[3]
5.
7x + 6 = 48
[3]
6.
7x + 2 = 16
[3]

Answer key

  1. x = −2Subtract 10 from both sides: 6x = −12; Divide by 6: x = −2
  2. x = 7Subtract 10 from both sides: 3x = 21; Divide by 3: x = 7
  3. x = 4Subtract 4 from both sides: 3x = 12; Divide by 3: x = 4
  4. x = 9Subtract 11 from both sides: 3x = 27; Divide by 3: x = 9
  5. x = 6Subtract 6 from both sides: 7x = 42; Divide by 7: x = 6
  6. x = 2Subtract 2 from both sides: 7x = 14; Divide by 7: x = 2