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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Six questions across Foundation, Standard and Extension, with full worked solutions, calibrated to the Victorian Curriculum.
Textbook questions won't lift a test mark.
They come sorted by topic, so your child knows the method before they read the question.
That's where Tuterly comes in and closes the gap: unlimited questions, mixed up, under test conditions, including worded problems.
- ✓Unlimited questions on entire topics, mixed difficulty, VCAA aligned
- ✓Printable test, plus a separate answer key for marking
- ✓Any topic, any time, designed to mimic actual test questions
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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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From our families
Parents on the practice questions.
“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”
Rebecca M.
Year 8 · Maths
“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”
Priya S.
Year 9 · Maths
“I like that I can just keep doing questions until it clicks. If I get something wrong, it shows me why, and then gives me another one like it.”
Ella, student
Year 10 · Maths
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.
Talk to a human
Talk to us about Year 7 linear equations.
Call or message us with your student's year level and what's tripping them up - we'll point you to the right tutor.