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2.3 Solving Equations Using the Subtraction and Addition Properties of Equality

Testing whether a number is a solution, then undoing an addition or subtraction on both sides to isolate the variable, with a balance model behind each step.

Prealgebra 2e, 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality

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56 exercises

2.3 Exercise 1

Before you get started, take this readiness quiz.

Evaluatex+8whenx=11.\text{Evaluate} x + 8 \text{when} x = 11 .
If you missed this problem, review the reference.

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2.3 Exercise 2

Evaluate5x−3whenx=9.\text{Evaluate} 5 x - 3 \text{when} x = 9 .
If you missed this problem, review the reference.

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2.3 Exercise 3

Translate into algebra: the difference of xx and 8.8 .
If you missed this problem, review the reference.

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2.3 Exercise 5

Isx=3a solution of4x−7=16?\text{Is} x = 3 \text{a solution of} 4 x - 7 = 16 ?

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2.3 Exercise 6

Isx=2a solution of6x−2=10?\text{Is} x = 2 \text{a solution of} 6 x - 2 = 10 ?

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2.3 Exercise 8

Isy=3a solution of9y−2=8y+1?\text{Is} y = 3 \text{a solution of} 9 y - 2 = 8 y + 1 ?

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2.3 Exercise 9

Isy=4a solution of5y−3=3y+5?\text{Is} y = 4 \text{a solution of} 5 y - 3 = 3 y + 5 ?

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2.3 Exercise 14

Solve:

x+6=19x + 6 = 19

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2.3 Exercise 15

Solve:

x+9=14x + 9 = 14

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2.3 Exercise 17

Solve:

95=y+6795 = y + 67

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2.3 Exercise 18

Solve:

91=y+4591 = y + 45

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2.3 Exercise 20

Solve:

x−9=13x - 9 = 13

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2.3 Exercise 21

Solve:

y−1=3y - 1 = 3

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2.3 Exercise 23

Solve:

19=a−1819 = a - 18

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2.3 Exercise 24

Solve:

27=n−1427 = n - 14

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2.3 Exercise 26

Translate the sentence into an algebraic equation:

The sum of 77 and 66 gives 13.13 .

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2.3 Exercise 27

Translate the sentence into an algebraic equation:

The sum of 88 and 66 is 14.14 .

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2.3 Exercise 29

Translate the sentence into an algebraic equation:

The product of 66 and 99 is 54.54 .

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2.3 Exercise 30

Translate the sentence into an algebraic equation:

The product of 2121 and 33 gives 63.63 .

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2.3 Exercise 32

Translate the given sentence into an algebraic equation:

Twice the difference of xx and 55 gives 30.30 .

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2.3 Exercise 33

Translate the given sentence into an algebraic equation:

Twice the difference of yy and 44 gives 16.16 .

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2.3 Exercise 35

Translate and solve:

Seven more than xx is equal to 37.37 .

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2.3 Exercise 36

Translate and solve:

Eleven more than yy is equal to 28.28 .

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2.3 Exercise 38

Translate and solve:

The difference of zz and 1717 is equal to 37.37 .

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2.3 Exercise 39

Translate and solve:

The difference of xx and 1919 is equal to 45.45 .

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2.3 Exercise 40

Determine whether each given value is a solution to the equation.

x+13=21x + 13 = 21

  1. ⓐ x=8x = 8
  2. ⓑ x=34x = 34

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2.3 Exercise 42

Determine whether each given value is a solution to the equation.

m−4=13m - 4 = 13

  1. ⓐ m=9m = 9
  2. ⓑ m=17m = 17

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2.3 Exercise 44

Determine whether each given value is a solution to the equation.

3p+6=153 p + 6 = 15

  1. ⓐ p=3p = 3
  2. ⓑ p=7p = 7

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2.3 Exercise 46

Determine whether each given value is a solution to the equation.

18d−9=2718 d - 9 = 27

  1. ⓐ d=1d = 1
  2. ⓑ d=2d = 2

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2.3 Exercise 48

Determine whether each given value is a solution to the equation.

8u−4=4u+408 u - 4 = 4 u + 40

  1. ⓐ u=3u = 3
  2. ⓑ u=11u = 11

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2.3 Exercise 50

Determine whether each given value is a solution to the equation.

20h−5=15h+3520 h - 5 = 15 h + 35

  1. ⓐ h=6h = 6
  2. ⓑ h=8h = 8

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2.3 Exercise 56

Solve each equation using the subtraction property of equality.

a+2=18a + 2 = 18

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2.3 Exercise 58

Solve each equation using the subtraction property of equality.

p+18=23p + 18 = 23

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2.3 Exercise 60

Solve each equation using the subtraction property of equality.

r+76=100r + 76 = 100

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2.3 Exercise 62

Solve each equation using the subtraction property of equality.

16=x+916 = x + 9

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2.3 Exercise 64

Solve each equation using the subtraction property of equality.

93=p+2493 = p + 24

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2.3 Exercise 66

Solve each equation using the subtraction property of equality.

465=d+398465 = d + 398

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2.3 Exercise 68

Solve each equation using the addition property of equality.

y−3=19y - 3 = 19

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2.3 Exercise 70

Solve each equation using the addition property of equality.

u−6=24u - 6 = 24

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2.3 Exercise 72

Solve each equation using the addition property of equality.

f−55=123f - 55 = 123

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2.3 Exercise 74

Solve each equation using the addition property of equality.

19=n−1319 = n - 13

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2.3 Exercise 76

Solve each equation using the addition property of equality.

10=p−3810 = p - 38

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2.3 Exercise 78

Solve each equation using the addition property of equality.

268=y−199268 = y - 199

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2.3 Exercise 80

Translate the given sentence into an algebraic equation.

The sum of 88 and 99 is equal to 17.17 .

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2.3 Exercise 82

Translate the given sentence into an algebraic equation.

The difference of 2323 and 1919 is equal to 4.4 .

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2.3 Exercise 84

Translate the given sentence into an algebraic equation.

The product of 33 and 99 is equal to 27.27 .

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2.3 Exercise 86

Translate the given sentence into an algebraic equation.

The quotient of 5454 and 66 is equal to 9.9 .

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2.3 Exercise 88

Translate the given sentence into an algebraic equation.

Twice the difference of nn and 1010 gives 52.52 .

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2.3 Exercise 90

Translate the given sentence into an algebraic equation.

The sum of three times yy and 1010 is 100.100 .

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2.3 Exercise 92

Translate the given sentence into an algebraic equation and then solve it.

Five more than pp is equal to 21.21 .

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2.3 Exercise 94

Translate the given sentence into an algebraic equation and then solve it.

The sum of rr and 1818 is 73.73 .

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2.3 Exercise 96

Translate the given sentence into an algebraic equation and then solve it.

The difference of dd and 3030 is equal to 52.52 .

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2.3 Exercise 98

Translate the given sentence into an algebraic equation and then solve it.

1212 less than uu is 89.89 .

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2.3 Exercise 100

Translate the given sentence into an algebraic equation and then solve it.

325325 less than cc gives 799.799 .

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2.3 Exercise 102

Insurance Vince’s car insurance has a $500\$\text{500} deductible. Find the amount the insurance company will pay, p,p , for an $1800\$\text{1800} claim by solving the equation 500+p=1800.500 + p = 1800 .

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2.3 Exercise 104

Sale purchase Arthur bought a suit that was on sale for $120\$\text{120} off. He paid $340\$\text{340} for the suit. Find the original price, p,p , of the suit by solving the equation p−120=340.p - 120 = 340 .

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