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Balancing Linear Equations Worksheet

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Balancing Linear Equations Worksheet

Solve each equation by keeping both sides balanced. Show your working where space is provided.

One-Step Equations

Use one inverse operation to find the unknown.

1.Solve: a + 9 = 23

2.Find b if 6b = 42.

3.Solve: c − 12 = 5

4.Find d if d ÷ 4 = 9.

Two-Step Equations

Undo the operations in reverse order to isolate the unknown.

5.Solve: 3p + 4 = 25

6.Solve: 5q − 6 = 29

7.Solve: 2r + 11 = 31

8.Which equation is true when x = 5?

2x + 3 = 13
3x − 4 = 10
x + 8 = 12
4x = 25

9.Match each equation with its solution.

2x + 1 = 11
3y − 2 = 10
4z + 3 = 19
5w − 5 = 15

y = 4
x = 5
z = 4
w = 4

Inequalities and Substitution

Use the inequality sign carefully. Substitute the given value wherever its variable appears.

10.Solve the inequality: t + 6 < 14

11.Solve the inequality: 3u ≥ 18

12.If v = 4, calculate 3v + 2.

13.Georgia has $31 to spend. A bus ticket costs $7, and each notebook costs $4. Write an inequality for the number n of notebooks she can buy, then find the greatest whole number of notebooks she can afford.

14.Select every value of k that makes 2k + 3 = 15 true.