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Solving Linear Equations

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Solving Linear Equations

Keep an equation balanced by doing the same operation to both sides. Show your working, then check solutions by substitution.

One-step equations

Find the value of the variable in each equation. Show your working.

1.Solve: a + 9 = 23

2.Solve: b − 8 = 6

3.Solve: 7c = 56

4.Solve: d ÷ 5 = 9

Two-step equations

Undo the addition or subtraction first, then undo the multiplication or division.

5.Solve: 3p + 4 = 25

6.Solve: 5q − 7 = 28

7.Solve: 32 = 4r + 8

8.Solve: 6s + 5 = 41

9.Which value of t makes 2t − 3 = 13 true?

t = 5
t = 8
t = 10
t = 16

10.Match each equation with the first operation that will help isolate its variable.

u + 12 = 20
v − 9 = 4
8w = 48
z ÷ 6 = 7

Add 9 to both sides
Multiply both sides by 6
Divide both sides by 8
Subtract 12 from both sides

Equations in everyday situations

Write an equation for each situation, solve it, and include the requested unit.

11.Ruben buys 5 identical notebooks and pays a $4 delivery charge. The total is $29. Let n be the price of one notebook. Write an equation and find n.

12.A kayak hire costs $18 per hour, plus a fixed equipment fee. For 3 hours, the total charge is $66. Let f be the equipment fee. Write an equation and calculate f.

13.Check your notebook answer by substituting n = 5 into 5n + 4 = 29. Show the calculation and state whether both sides are equal.