Explains the balance method for solving equations: do the same thing to both sides using inverse operations. Builds from one-step equations to two-step equations, equations with brackets and equations with pronumerals on both sides, with a check-by-substitution habit throughout.
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Curriculum: Australian Curriculum. We show specific outcome codes only where they have been verified against the official curriculum document.
Completed: Solving Linear Equations
Year 8 students (typically ages 13–14) working on linear equations. It is pitched at level 2 · standard.
This is a study guide, so there is no separate answer sheet; the 'Check yourself' questions include answers.
About 20 minutes. Short, regular sessions work best: two or three a week beats one long one.
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Try Year 8 Solving Linear Equations Worksheet — Level 2, then check understanding with the Year 8 Linear Equations Topic Test.
Year 8 · Mathematics · Linear Equations
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An equation says that two expressions are equal, like 3x + 5 = 20. To solve it means to find the value of the pronumeral that makes the statement true. Think of the equals sign as the middle of a balance scale: whatever you do to one side, you must do to the other, or the scale tips. Your goal is to get the pronumeral by itself on one side.
To undo an operation, use its inverse. Work backwards through the order of operations: undo any adding or subtracting first, then undo multiplying or dividing.
| Operation in the equation | Undo it with |
|---|---|
| + 7 | − 7 |
| − 3 | + 3 |
| × 4 (as in 4x) | ÷ 4 |
| ÷ 5 (as in ) | × 5 |
One-step: x + 7 = 12 and 4x = 28
Two-step: 3x + 5 = 20
With a fraction: − 2 = 3
With brackets: 2(x + 3) = 14
Pronumerals on both sides: 5x − 3 = 2x + 9
Answers: 1. x = 13 2. x = 9 3. x = 7 4. x = 15 5. x = 6 6. x = 7
Preview — the PDF contains the full resource.
One-step, two-step and equations with brackets or variables on both sides. Expected-level practice for this year group. This Year 8…
One-step, two-step and equations with brackets or variables on both sides. Expected-level practice for this year group. This Year 8…
One-step, two-step and equations with brackets or variables on both sides. A challenge set for students ready to stretch further. This…
Two-step equations, equations with brackets and expanding brackets in a 40-minute Year 8 test with marks and worked solutions.
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