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

Solve, simplify and describe algebraic patterns. Show your working where space is provided. Check equation solutions by substituting them back into the original equation.

Solve the Equations

Use inverse operations to find each unknown. Show a few steps and check by substitution.

1.Find the value of a in a + 8 = 17.

2.Solve 5b = 35.

3.Solve 3c + 4 = 19.

4.Find d if 4d − 6 = 18.

5.Solve 7e = 56.

6.Find f if 2f + 9 = 25.

Simplify the Expressions

Expand any brackets, then combine terms with the same variable part.

7.Simplify 2(x + 6) + 3.

8.Simplify 3(m + 2) − m.

9.Write 7 + (4y − 3) as a simplified expression.

10.Expand and simplify 5(p − 2) + 2p.

11.Simplify 2(4k + 3) − 5.

Patterns and Rules

Look for how the terms change from one position to the next. Use n for the position number when writing a rule.

12.The sequence begins 4, 9, 14, 19. Write the next two terms.

13.A sequence starts 6, 12, 18, 24, ... . Write a rule for its term at position n.

14.For the sequence with rule 6n, calculate the term at position 9.

Position n

Value

___

15.For the sequence table above, fill in the value at position 4 and give an algebraic rule for the value at position n.

16.A woven design has 4 diamonds in its first row and gains 3 diamonds for each increase of one row. If row number is n, the rule is 3n + 1. How many diamonds are in row 7?

Equations in Everyday Situations

Choose a variable, write an equation from the information, then solve it.

17.Luca had some trading cards. He gave 9 away and now has 18. Let s be the number he had at first. Write an equation and find s.

18.A rectangle is 3 times as long as it is wide. Its perimeter is 40 cm. If its width is w centimetres, write an equation and work out the width.

19.A community bike hire charges $12 to start, then $6 for each hour. The total bill was $42. Let h be the number of hours. Write an equation and find h.