<< Chapter < Page Chapter >> Page >

Practice makes perfect

Solve Equations Using the Subtraction and Addition Properties of Equality

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

Is y = 1 3 a solution of 4 y + 2 = 10 y ?

yes

Got questions? Get instant answers now!

Is x = 3 4 a solution of 5 x + 3 = 9 x ?

Got questions? Get instant answers now!

Is u = 1 2 a solution of 8 u 1 = 6 u ?

no

Got questions? Get instant answers now!

Is v = 1 3 a solution of 9 v 2 = 3 v ?

Got questions? Get instant answers now!

In the following exercises, solve each equation.

p + 2.4 = −9.3

p = −11.7

Got questions? Get instant answers now!

x 15 = −42

x = −27

Got questions? Get instant answers now!

q + 3 4 = 1 2

q = 1 4

Got questions? Get instant answers now!

y 3 4 = 3 5

y = 27 20

Got questions? Get instant answers now!

Solve Equations that Need to be Simplified

In the following exercises, solve each equation.

9 x + 5 8 x + 14 = 20

Got questions? Get instant answers now!

6 x + 8 5 x + 16 = 32

8

Got questions? Get instant answers now!

−6 x 11 + 7 x 5 = −16

Got questions? Get instant answers now!

−8 n 17 + 9 n 4 = −41

−20

Got questions? Get instant answers now!

3 ( y 5 ) 2 y = −7

Got questions? Get instant answers now!

4 ( y 2 ) 3 y = −6

2

Got questions? Get instant answers now!

8 ( u + 1.5 ) 7 u = 4.9

Got questions? Get instant answers now!

5 ( w + 2.2 ) 4 w = 9.3

1.7

Got questions? Get instant answers now!

−5 ( y 2 ) + 6 y = −7 + 4

Got questions? Get instant answers now!

−8 ( x 1 ) + 9 x = −3 + 9

−2

Got questions? Get instant answers now!

3 ( 5 n 1 ) 14 n + 9 = 1 2

Got questions? Get instant answers now!

2 ( 8 m + 3 ) 15 m 4 = 3 5

−4

Got questions? Get instant answers now!

( j + 2 ) + 2 j 1 = 5

Got questions? Get instant answers now!

( k + 7 ) + 2 k + 8 = 7

6

Got questions? Get instant answers now!

6 a 5 ( a 2 ) + 9 = −11

Got questions? Get instant answers now!

8 c 7 ( c 3 ) + 4 = −16

−41

Got questions? Get instant answers now!

8 ( 4 x + 5 ) 5 ( 6 x ) x = 53

Got questions? Get instant answers now!

6 ( 9 y 1 ) 10 ( 5 y ) 3 y = 22

28

Got questions? Get instant answers now!

Translate to an Equation and Solve

In the following exercises, translate to an equation and then solve.

Five more than x is equal to 21 .

Got questions? Get instant answers now!

The sum of x and −5 is 33 .

x + (−5) = 33; x = 38

Got questions? Get instant answers now!

Ten less than m is −14 .

Got questions? Get instant answers now!

Three less than y is −19 .

y − 3 = −19; y = −16

Got questions? Get instant answers now!

The sum of y and −3 is 40 .

Got questions? Get instant answers now!

Eight more than p is equal to 52 .

p + 8 = 52; p = 44

Got questions? Get instant answers now!

The difference of 9 x and 8 x is 17 .

Got questions? Get instant answers now!

The difference of 5 c and 4 c is 60 .

5 c − 4 c = 60; 60

Got questions? Get instant answers now!

The difference of n and 1 6 is 1 2 .

Got questions? Get instant answers now!

The difference of f and 1 3 is 1 12 .

f 1 3 = 1 12 ; 5 12

Got questions? Get instant answers now!

The sum of −4 n and 5 n is −32 .

Got questions? Get instant answers now!

The sum of −9 m and 10 m is −25 .

−9 m + 10 m = −25; m = −25

Got questions? Get instant answers now!

Translate and Solve Applications

In the following exercises, translate into an equation and solve.

Pilar drove from home to school and then to her aunt’s house, a total of 18 miles. The distance from Pilar’s house to school is 7 miles. What is the distance from school to her aunt’s house?

Got questions? Get instant answers now!

Jeff read a total of 54 pages in his English and Psychology textbooks. He read 41 pages in his English textbook. How many pages did he read in his Psychology textbook?

Let p equal the number of pages read in the Psychology book 41 + p = 54. Jeff read pages in his Psychology book.

Got questions? Get instant answers now!

Pablo’s father is 3 years older than his mother. Pablo’s mother is 42 years old. How old is his father?

Got questions? Get instant answers now!

Eva’s daughter is 5 years younger than her son. Eva’s son is 12 years old. How old is her daughter?

Let d equal the daughter’s age. d = 12 − 5. Eva’s daughter’s age is 7 years old.

Got questions? Get instant answers now!

Allie weighs 8 pounds less than her twin sister Lorrie. Allie weighs 124 pounds. How much does Lorrie weigh?

Got questions? Get instant answers now!

For a family birthday dinner, Celeste bought a turkey that weighed 5 pounds less than the one she bought for Thanksgiving. The birthday dinner turkey weighed 16 pounds. How much did the Thanksgiving turkey weigh?

21 pounds

Got questions? Get instant answers now!

The nurse reported that Tricia’s daughter had gained 4.2 pounds since her last checkup and now weighs 31.6 pounds. How much did Tricia’s daughter weigh at her last checkup?

Got questions? Get instant answers now!

Connor’s temperature was 0.7 degrees higher this morning than it had been last night. His temperature this morning was 101.2 degrees. What was his temperature last night?

100.5 degrees

Got questions? Get instant answers now!

Melissa’s math book cost $22.85 less than her art book cost. Her math book cost $93.75 . How much did her art book cost?

Got questions? Get instant answers now!

Ron’s paycheck this week was $17.43 less than his paycheck last week. His paycheck this week was $103.76 . How much was Ron’s paycheck last week?

$121.19

Got questions? Get instant answers now!

Everyday math

Baking Kelsey needs 2 3 cup of sugar for the cookie recipe she wants to make. She only has 1 4 cup of sugar and will borrow the rest from her neighbor. Let s equal the amount of sugar she will borrow. Solve the equation 1 4 + s = 2 3 to find the amount of sugar she should ask to borrow.

Got questions? Get instant answers now!

Construction Miguel wants to drill a hole for a 5 8 -inch screw. The screw should be 1 12 inch larger than the hole. Let d equal the size of the hole he should drill. Solve the equation d + 1 12 = 5 8 to see what size the hole should be.

d = 13 24

Got questions? Get instant answers now!

Writing exercises

Is −18 a solution to the equation 3 x = 16 5 x ? How do you know?

Got questions? Get instant answers now!

Write a word sentence that translates the equation y 18 = 41 and then make up an application that uses this equation in its solution.

Answers will vary.

Got questions? Get instant answers now!

Self check

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

.

If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Practice Key Terms 1

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Prealgebra' conversation and receive update notifications?

Ask