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2.3 Solve Equations with Variables and Constants on Both Sides

Collecting variable terms on one side and constants on the other, and choosing which side to clear first to keep the coefficient positive.

Elementary Algebra 2e, 2.3 Solve Equations with Variables and Constants on Both Sides

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50 exercises

2.3 Exercise 1

Before you get started, take this readiness quiz.

Simplify: 4y−9+9.4 y - 9 + 9 .
If you missed this problem, review the reference.

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2.3 Exercise 3

Solve: 3x+4=−8.3 x + 4 = −8 .

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2.3 Exercise 4

Solve: 5a+3=−37.5 a + 3 = −37 .

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2.3 Exercise 6

Solve: 5y−9=16.5 y - 9 = 16 .

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2.3 Exercise 7

Solve: 3m−8=19.3 m - 8 = 19 .

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2.3 Exercise 9

Solve: 6n=5n−10.6 n = 5 n - 10 .

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2.3 Exercise 10

Solve: −6c=−7c−1.−6 c = −7 c - 1 .

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2.3 Exercise 12

Solve: 3p−14=5p.3 p - 14 = 5 p .

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2.3 Exercise 13

Solve: 8m+9=5m.8 m + 9 = 5 m .

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2.3 Exercise 15

Solve: 12j=−4j+32.12 j = −4 j + 32 .

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2.3 Exercise 16

Solve: 8h=−4h+12.8 h = −4 h + 12 .

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2.3 Exercise 18

Solve: 12x+8=6x+2.12 x + 8 = 6 x + 2 .

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2.3 Exercise 19

Solve: 9y+4=7y+12.9 y + 4 = 7 y + 12 .

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2.3 Exercise 21

Solve: 8q−5=−4q+7.8 q - 5 = −4 q + 7 .

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2.3 Exercise 22

Solve: 7n−3=n+3.7 n - 3 = n + 3 .

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2.3 Exercise 24

Solve: 2a−2=6a+18.2 a - 2 = 6 a + 18 .

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2.3 Exercise 25

Solve: 4k−1=7k+17.4 k - 1 = 7 k + 17 .

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2.3 Exercise 27

Solve: 78x−12=−18x−2.\frac{7}{8} x - 12 = - \frac{1}{8} x - 2 .

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2.3 Exercise 28

Solve: 76y+11=16y+8.\frac{7}{6} y + 11 = \frac{1}{6} y + 8 .

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2.3 Exercise 30

Solve: 2.8x+12=−1.4x−9.2.8 x + 12 = −1.4 x - 9 .

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2.3 Exercise 31

Solve: 3.6y+8=1.2y−4.3.6 y + 8 = 1.2 y - 4 .

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2.3 Exercise 33

Solve the following equations with constants on both sides.

12x−8=6412 x - 8 = 64

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2.3 Exercise 35

Solve the following equations with constants on both sides.

15y+7=9715 y + 7 = 97

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2.3 Exercise 37

Solve the following equations with constants on both sides.

3m+9=−153 m + 9 = −15

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2.3 Exercise 39

Solve the following equations with constants on both sides.

−77=9b−5−77 = 9 b - 5

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2.3 Exercise 41

Solve the following equations with constants on both sides.

60=−21x−2460 = −21 x - 24

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2.3 Exercise 43

Solve the following equations with constants on both sides.

−14q−2=16−14 q - 2 = 16

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2.3 Exercise 45

Solve the following equations with variables on both sides.

21k=20k−1121 k = 20 k - 11

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2.3 Exercise 47

Solve the following equations with variables on both sides.

8x+27=11x8 x + 27 = 11 x

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2.3 Exercise 49

Solve the following equations with variables on both sides.

b=−4b−15b = −4 b - 15

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2.3 Exercise 51

Solve the following equations with variables on both sides.

5z=39−8z5 z = 39 - 8 z

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2.3 Exercise 53

Solve the following equations with variables on both sides.

4x+34=3x4 x + \frac{3}{4} = 3 x

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2.3 Exercise 55

Solve the following equations with variables on both sides.

−11r−8=−7r−11 r - 8 = −7 r

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2.3 Exercise 57

Solve the following equations with variables and constants on both sides.

6x−17=5x+26 x - 17 = 5 x + 2

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2.3 Exercise 59

Solve the following equations with variables and constants on both sides.

21+18f=19f+1421 + 18 f = 19 f + 14

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2.3 Exercise 61

Solve the following equations with variables and constants on both sides.

12q−5=9q−2012 q - 5 = 9 q - 20

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2.3 Exercise 63

Solve the following equations with variables and constants on both sides.

8c+7=−3c−378 c + 7 = −3 c - 37

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2.3 Exercise 65

Solve the following equations with variables and constants on both sides.

7x−17=−8x+137 x - 17 = −8 x + 13

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2.3 Exercise 67

Solve the following equations with variables and constants on both sides.

9p+14=6+4p9 p + 14 = 6 + 4 p

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2.3 Exercise 69

Solve the following equations with variables and constants on both sides.

3y−4=12−y3 y - 4 = 12 - y

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2.3 Exercise 71

Solve the following equations with variables and constants on both sides.

74m−7=34m−13\frac{7}{4} m - 7 = \frac{3}{4} m - 13

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2.3 Exercise 73

Solve the following equations with variables and constants on both sides.

11−15a=45a+411 - \frac{1}{5} a = \frac{4}{5} a + 4

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2.3 Exercise 75

Solve the following equations with variables and constants on both sides.

54a+15=34a−5\frac{5}{4} a + 15 = \frac{3}{4} a - 5

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2.3 Exercise 77

Solve the following equations with variables and constants on both sides.

35p+2=45p−1\frac{3}{5} p + 2 = \frac{4}{5} p - 1

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2.3 Exercise 79

Solve the following equations with variables and constants on both sides.

13z+6.45=8z+23.7513 z + 6.45 = 8 z + 23.75

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2.3 Exercise 81

Solve the following equations with variables and constants on both sides.

2.7w−80=1.2w+102.7 w - 80 = 1.2 w + 10

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2.3 Exercise 83

Solve the following equations with variables and constants on both sides.

6.6x−18.9=3.4x+54.76.6 x - 18.9 = 3.4 x + 54.7

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2.3 Exercise 85

Making a fence Jovani has 150 feet of fencing to make a rectangular garden in his backyard. He wants the length to be 15 feet more than the width. Find the width, w, by solving the equation 150=2w+30+2w150 = 2 w + 30 + 2 w.

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2.3 Exercise 87

Solve the equation 10x+14=−2x+3810 x + 14 = −2 x + 38 explaining all the steps of your solution as in the examples in this section.

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2.3 Exercise 89

Is x=−2x = −2 a solution to the equation 5−2x=−4x+15 - 2 x = −4 x + 1 ? How do you know?

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Adapted from Elementary Algebra 2e © 2020 Rice University. Licensed under CC BY 4.0. Source: Elementary Algebra 2e. Imported at revision 77a933c.