Year 7 - Linear equations - Free practice
Year 7 Linear Equations Worksheets & Practice Tests
Solve for x with confidence. Worked solutions every time, free.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
About this worksheet
Why we built it
Linear equations are the first real "do the same thing to both sides" topic in Year 7 maths. These worksheets give your student a steady ramp from one-step equations to two- and three-step problems, with worked solutions for every question so they can see exactly where their working breaks.
What's covered
Sub-skills your student will practise
- ✓One-step equations (x + 7 = 12, 3x = 18)
- ✓Two-step equations (2x + 5 = 17)
- ✓Equations with brackets (3(x + 2) = 21)
- ✓Word problems that translate into a linear equation
- ✓Verifying solutions by substitution
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Frequently asked
Questions parents ask about linear equations
What kind of linear equations does Year 7 cover?
Year 7 focuses on one-variable equations with natural number solutions - so things like 2x + 5 = 17 and 3(x + 4) = 21, but not yet equations with negative or fractional solutions. The aim is fluency with the 'do the same to both sides' move.
What order should students solve linear equations in?
Undo the operations in reverse PEMDAS order: cancel addition or subtraction first, then multiplication or division. For an equation like 2x + 5 = 17, subtract 5 from both sides first, then divide by 2.
Why do students get linear equations wrong even when they understand the steps?
Usually it's signs and operations on negatives - especially when subtracting on both sides. The other common slip is forgetting to expand brackets before collecting like terms. These worksheets mix both formats so students can't just apply one pattern.
Do students need to know how to graph linear equations in Year 7?
Year 7 introduces patterns on the Cartesian plane and tables of values, but full y = mx + c graphing properly arrives in Year 8. For now, plotting points from a rule is the main graphing skill.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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Talk to us about Year 7 linear equations.
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