MathsFreePrintable

Linear Equations Practice

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Linear Equations Practice

Form an equation for each situation, then solve where asked. Show your working and check solutions by substitution.

Forming Equations from Situations

1.A bike hire shop charges a fixed fee of $6 plus $2.50 for each hour. The total bill is $21. Write an equation to find h, the number of hours hired.

2.Rawiri buys 4 identical notebooks and a $3 pen. She spends $19 altogether. Write an equation to find n, the price of one notebook.

3.A monthly data plan costs $18 plus $0.25 for each extra gigabyte used. The bill is $26. Write an equation to find g, the number of extra gigabytes.

Solving One-Step Equations

4.Solve: p + 9 = 22

5.Solve: 7q = 56

6.Solve: r − 11 = 6

7.Solve: s ÷ 5 = 9

Solving Two-Step Equations

8.Solve: 4a + 3 = 27

9.Solve: 3b − 8 = 13

10.Solve: 5c + 6 = 41

11.Solve: 6d − 7 = 29

Checking Solutions

12.Test whether x = 5 satisfies 3x + 2 = 17. Substitute the value and decide if both sides are equal.

Yes, x = 5 is a solution
No, x = 5 is not a solution

13.Test whether y = 4 satisfies 2y − 3 = 8. Substitute the value and decide if both sides are equal.

Yes, y = 4 is a solution
No, y = 4 is not a solution

Algebra Vocabulary

14.Match each algebra term to its meaning.

Variable
Coefficient
Constant
Inverse operation

A number multiplied by a variable
A letter representing an unknown or changing value
A value that stays fixed
An operation that undoes another operation

15.Which two pairs are inverse operations? Select all that apply.

Addition and subtraction
Multiplication and division
Addition and multiplication
Subtraction and division

Problem-Solving Challenge

16.A community group sells raffle tickets for $4 each. After paying $20 for printing, it has $76 left over. Let t be the number of tickets sold. Write an equation and solve it. Show a check of your answer.

17.For the equation 3m + 8 = 26, state which inverse operation you would use first and explain why. Then state the next operation needed to find m.