Year 7 - Linear equations - Free practice

Year 7 Linear Equations Worksheets & Practice Tests

Solve for x with confidence. Worked solutions every time, free.

Quick answer

How do you solve linear equations in Year 7?

To solve a one-variable linear equation, use inverse operations to get the pronumeral alone on one side. For a two-step equation like 2x + 5 = 17, subtract 5 from both sides to get 2x = 12, then divide both sides by 2 to get x = 6. Always check by substituting your answer back in.

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Worked examples

Year 7 linear equations: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Two-step equations
Solve $2x + 5 = 17$ , then verify your solution by substitution.
Show worked solution
Key idea: Undo the operations in reverse order, subtract first, then divide.
1. Subtract $5$ from both sides:
  $2x + 5 - 5 = 17 - 5 \implies 2x = 12$
2. Divide both sides by $2$ :
  $x = \frac{12}{2} = 6$
3. Verify by substituting $x = 6$ back into the original equation:
  $2(6) + 5 = 12 + 5 = 17 \checkmark$
Answer: $x = 6$
Example 2 · Equations with brackets
Solve $3(x + 2) = 21$ .
Show worked solution
Key idea: Expand the brackets first, then solve the two-step equation.
1. Expand the brackets:
  $3(x + 2) = 3x + 6$ So the equation becomes $3x + 6 = 21$ .
2. Subtract $6$ from both sides:
  $3x = 21 - 6 = 15$
3. Divide both sides by $3$ :
  $x = \frac{15}{3} = 5$
4. Verify by substituting $x = 5$ into the original equation:
  $3(5 + 2) = 3 \times 7 = 21 \checkmark$
Answer: $x = 5$
Example 3 · Word problem, equations from a real-life situation
Aisha is saving up to buy a book that costs $29. She already has $11 saved and earns $6 per hour doing odd jobs. How many hours does Aisha need to work to have exactly enough money to buy the book?
Show worked solution
Key idea: Translate the situation into a linear equation, solve it, then verify.
1. Let $h$ be the number of hours Aisha needs to work. Her total savings will be $6h + 11$ dollars. Set this equal to $29$ :
  $6h + 11 = 29$
2. Subtract $11$ from both sides:
  $6h = 29 - 11 = 18$
3. Divide both sides by $6$ :
  $h = \frac{18}{6} = 3$
4. Verify by substituting $h = 3$ :
  $6(3) + 11 = 18 + 11 = 29 \checkmark$
Answer: Aisha needs to work $3$ hours.

Common mistakes

Where students usually lose marks

Dividing before subtracting in a two-step equation

$2x + 5 = 17 \implies x + 5 = 8.5$ (divided by $2$ first)

Always undo addition or subtraction before multiplication or division. Subtract the constant term from both sides first, then divide.

Forgetting to expand brackets fully

$3(x + 2) = 21 \implies 3x + 2 = 21$ (only multiplied the $x$ , not the $2$ )

Every term inside the brackets must be multiplied by the number outside. Here, $3(x + 2) = 3 \times x + 3 \times 2 = 3x + 6$ .

Not applying the operation to both sides

$2x = 12 \implies 2x - 2 = 12$ (subtracted $2$ from the left side only)

Whatever you do to one side of an equation, you must do exactly the same to the other side. This keeps the equation balanced.

Skipping or rushing the substitution check

Substituting $x = 5$ into $2x + 5 = 17$ gives $2(5) = 10$ , so it checks out. (forgot to add the $5$ )

Replace every $x$ with the answer and evaluate the full expression step by step. Only tick the answer if both sides give exactly the same number.

Try one yourself

Your turn

Solve the equation $3(x + 2) = 21$ . What is the value of $x$ ?

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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

From our families

Parents on the practice questions.

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Year 9 · Maths

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Year 10 · Maths

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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.

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