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Equations and Inequalities Practice

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Equations and Inequalities Practice

Solve linear equations and one-variable inequalities, check solutions by substitution, and use equations to solve problems. Show your working. When solving an inequality, remember that multiplying or dividing by a negative number reverses the inequality sign.

A. Linear equations

Solve each equation. Show enough working to make your method clear.

1.Find the value of a: a + 9 = 22

2.Solve for b: b − 6 = 11

3.Solve: 5c = 35

4.Find d: d ÷ 3 = 9

5.Solve for x: 4x + 3 = 27

6.Find y: 6y − 5 = 31

7.Solve: 2(p + 5) = 26

8.Find q: 3(q − 2) = 21

9.Solve for r: 5r + 4 = 2r + 25

10.Find s: 7s − 8 = 3s + 20

11.Solve: 3(t + 4) = 2t + 19

12.Find u: 2(3u − 1) = 4u + 14

B. Inequalities

Solve each inequality. Give your solution using an inequality symbol.

13.Solve: x + 5 > 12

14.Find all values of y that satisfy 4y ≤ 28.

15.Solve: 2m − 9 < 5

16.Solve: 7 − 3n ≥ 16

17.Solve 2k + 1 > 9, then show the solution on the number line.

C. Equations in context

Write or use an equation to solve each problem. Lighthouse settings are used for these scenarios.

18.At a lighthouse, Lachlan counts 9 seabirds before another group arrives. There are 26 seabirds altogether. How many were in the second group?

19.Cooper records that 4 identical signal flashes and 3 extra flashes make 31 flashes in total. How many flashes were in each identical group?

20.Omar has $60 for lighthouse supplies. He spends $12 on a torch and buys several batteries for $4 each. If $20 remains, how many batteries did he buy?

21.A rectangular viewing platform has a perimeter of 34 m. Its length is 3 m more than its width. Find the length and width.