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Determine Whether a Number is a Solution of an Equation

In the following exercises, determine whether each given value is a solution to the equation.

x + 13 = 21

  1. x = 8
  2. x = 34

  1. yes
  2. no

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y + 18 = 25

  1. y = 7
  2. y = 43

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m 4 = 13

  1. m = 9
  2. m = 17

  1. no
  2. yes

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n 9 = 6

  1. n = 3
  2. n = 15

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3 p + 6 = 15

  1. p = 3
  2. p = 7

  1. yes
  2. no

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8 q + 4 = 20

  1. q = 2
  2. q = 3

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18 d 9 = 27

  1. d = 1
  2. d = 2

  1. no
  2. yes

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24 f 12 = 60

  1. f = 2
  2. f = 3

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8 u 4 = 4 u + 40

  1. u = 3
  2. u = 11

  1. no
  2. yes

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7 v 3 = 4 v + 36

  1. v = 3
  2. v = 11

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20 h 5 = 15 h + 35

  1. h = 6
  2. h = 8

  1. no
  2. yes

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18 k 3 = 12 k + 33

k = 1

k = 6

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Model the Subtraction Property of Equality

In the following exercises, write the equation modeled by the envelopes and counters and then solve using the subtraction property of equality.

Solve Equations using the Subtraction Property of Equality

In the following exercises, solve each equation using the subtraction property of equality.

Solve Equations using the Addition Property of Equality

In the following exercises, solve each equation using the addition property of equality.

Translate Word Phrase to Algebraic Equations

In the following exercises, translate the given sentence into an algebraic equation.

The sum of 8 and 9 is equal to 17 .

8 + 9 = 17

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The sum of 7 and 9 is equal to 16 .

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The difference of 23 and 19 is equal to 4 .

23 − 19 = 4

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The difference of 29 and 12 is equal to 17 .

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The product of 3 and 9 is equal to 27 .

3 ⋅ 9 = 27

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The product of 6 and 8 is equal to 48 .

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The quotient of 54 and 6 is equal to 9 .

54 ÷ 6 = 9

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The quotient of 42 and 7 is equal to 6 .

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Twice the difference of n and 10 gives 52 .

2( n − 10) = 52

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Twice the difference of m and 14 gives 64 .

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The sum of three times y and 10 is 100 .

3 y + 10 = 100

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The sum of eight times x and 4 is 68 .

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Translate to an Equation and Solve

In the following exercises, translate the given sentence into an algebraic equation and then solve it.

Five more than p is equal to 21 .

p + 5 = 21; p = 16

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Nine more than q is equal to 40 .

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The sum of r and 18 is 73 .

r + 18 = 73; r = 55

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The sum of s and 13 is 68 .

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The difference of d and 30 is equal to 52 .

d − 30 = 52; d = 82

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The difference of c and 25 is equal to 75 .

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12 less than u is 89 .

u − 12 = 89; u = 101

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325 less than c gives 799 .

c − 325 = 799; c = 1124

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299 less than d gives 850 .

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Everyday math

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

$1300

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Insurance Marta’s homeowner’s insurance policy has a $750 deductible. The insurance company paid $5800 to repair damages caused by a storm. Find the total cost of the storm damage, d , by solving the equation d 750 = 5800 .

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

$460

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Sale purchase Rita bought a sofa that was on sale for $1299 . She paid a total of $1409 , including sales tax. Find the amount of the sales tax, t , by solving the equation 1299 + t = 1409 .

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Writing exercises

Is x = 1 a solution to the equation 8 x 2 = 16 6 x ? How do you know?

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Write the equation y 5 = 21 in words. Then make up a word problem for this equation.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

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What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Practice Key Terms 1

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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