Solve Problems with Inequalities Nameimages.pcmac.org/.../Documents/Lesson_17_HW.pdf · Solve Two-Step Inequalities Study the example showing how to solve a two-step inequality. Then

©Curriculum Associates, LLC Copying is not permitted. 171Lesson 17 Solve Problems with Inequalities

Name: Solve Problems with Inequalities

Lesson 17

Solve Problems with Equations

Study the example showing how to solve problems with equations. Then solve problems 1–8.

1 Why is 3 1 ·· 2 multiplied by x in the equation?

2 How can you get 3 1 ·· 2 x alone on the left side of the

equation 3 1 ·· 2 x 1 215 5 495? What is the resulting

equation?

3 Multiply both sides of the simplified equation you wrote in problem 2 by a fraction to get x alone on the left side of the equation Simplify

4 What is the charge for an hour of labor?

5 Explain how to solve the equation 3 ·· 4 x 1 5 5 11

Example

Mrs Scott brings her car to a service station for repair Her

bill shows a $215 charge for parts and a charge for 3 1 ·· 2 hours

of labor The total bill is $495 Write an equation to find the charge x for one hour of labor

Charge for labor 1 Charge for parts 5 Total bill

3 1 ·· 2 x 1 215 5 495

©Curriculum Associates, LLC Copying is not permitted.172 Lesson 17 Solve Problems with Inequalities

Solve.

6 Mito bakes biscuits He uses 1 ·· 4 cup of flour to coat the

countertop and the rolling pin He also uses 2 1 ·· 2 cups of

flour for each batch of biscuits he bakes If he uses

7 3 ·· 4 cups of flour in all, how many batches of biscuits

does he bake? Write and solve an equation

Show your work.

Solution:

7 The formula to convert a temperature C in degrees Celsius to a temperature F in degrees Fahrenheit is 1 8C 1 32 5 F Use this equation to find the Celsius equivalent of 51 8°F

8 LeBron mows yards For each yard, he charges $5 50 for the use of his mower and $3 50 for the use of his trimmer In addition, LeBron charges $5 00 an hour to mow and $6 50 an hour to trim

LeBron both mows and trims Mr Johnson’s lawn, using his own mower and trimmer He takes twice as long to mow as he does to trim If he earns $25 50 that day, how many hours did he mow?

Show your work.

Solution:


Name: Lesson 17

Solve Two-Step Inequalities

Study the example showing how to solve a two-step inequality. Then solve problems 1–7.

1 Use this number line to show numbers in the solution set of the inequality 2s 1 36 . 50

2 Do fractional solutions make sense in this context? Why or why not?

3 Explain why negative integers are not in the solution set

4 Explain why Ben would not meet his goal if he sold 7 cards How could his goal be rephrased to include 7 cards?

Example

Ben sells handmade cards at a craft fair He wants to earn more than $50 at the fair He sells his cards for $2 and has already earned $36 How many cards does he need to sell to reach his goal?

You can write an inequality that shows the number of cards, c, that Ben needs to sell to reach his goal

2c 1 36 . 50

To solve, first subtract 36 from both sides of the inequality

2c 1 36 2 36 . 50 2 36

Simplify 2c . 14

Divide both sides of the inequality by 2 2c ·· 2 . 14 ·· 2

Simplify c . 7

Ben needs to sell more than 7 cards to reach his goal

210 3 4 5 6 7 8 1211109


Solve.

5 Solve 2y 1 12 , 42

Show your work.

Solution:

6 Manuela works as a security guard She makes $15 per hour Her employers deduct $125 from her weekly check to cover insurance and taxes If Manuela receives at least $205 in her weekly paycheck, what is the fewest number of hours she works in a week? Write and solve an inequality

Show your work.

Solution:

7 What non-negative integers are solutions of the inequality u2x 2 1u , 3?

Show your work.

Solution:


Name: Lesson 17

Solve Multi-Step Inequalities

Study the example problem showing how to solve a multi-step inequality. Then solve problems 1–5.

1 Graph the solution set on the number line

2 Solve 6(3 1 n) , 48

Show your work.

Solution:

Example

Five family members are going to a play A service charge of $2 is added to the cost of each ticket The family is willing to pay $250 or less for the five tickets What is the greatest amount the family is willing to pay for each ticket?

You can write an inequality to represent the problem

Number • Cost Is less than or Total cost

of people per person equal to

5 • (x 1 2) # 250

5(x 1 2) # 250

5x 1 10 # 250

5x 1 10 2 10 # 250 2 10

5x # 240

5x ·· 5 # 240 ··· 5

x # 48

The family is willing to pay $48 or less for a ticket

3020 40 50 60


Solve.

3 Solve 6 1 2 ·· 3 x 2 3 2 . 8

Show your work.

Solution:

4 Graph the solution set of the inequality 3(1 2 x) , 9 Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality sign

5 Tiffany makes scarves and sells them at a neighborhood clothing store The owner charges her $25 a day for the space she uses She sells each scarf for $30 Each scarf costs her $14 to make How many scarves must Tiffany sell per day to make a profit of at least $100 per day? Write and solve an inequality

Show your work.

Solution:


Name:

1 Ms Kwan is making sandwiches for a class picnic She

prepares 1 1 ·· 2 sandwiches for each student in the class

and 4 more sandwiches in case there are guests Which inequality shows how many students, s, are in the class if Ms Kwan prepares no fewer than 49 sandwiches?

A s . 30 C s , 30

B s $ 30 D s # 30

Sam chose D as the correct answer How did he get that answer?

Solve Problems with Inequalities

Solve the problems.

3 Solve 4(24x 2 3) . 36

Show your work.

Solution:

2 Cindy and her younger sister have a total of less than $15 Cindy has twice as much money as her younger sister Let x represent the amount of money Cindy’s younger sister has Tell whether each statement is True or False

a. The inequality x 1 2x , 15 can be used to solve for x u True u False

b. The inequality x 1 2x $ 15 can be used to solve for x u True u False

c. Cindy could have $7 u True u False

d. Cindy’s younger sister could have $7 u True u False

Look for words in the problem that help you answer the question.

How can you represent the amount of money Cindy has?

Be sure to follow the correct order of operations.

Lesson 17


6 Which inequalities have the solution set shown on the number line? Select all that apply

A 5 ·· 4 x 1 1 ·· 8 # 2

B 1 4x 2 0 08 , 2 02

C 4 2 x . 2 1 ·· 2

D 2(x 2 5) # 27

Solve.

4 Gale’s grade in science for the term is determined by the average of five test grades His first four grades are 80, 95, 78, and 90 In order to get a B for the term, Gale needs to have an average of 84 What grade must Gale get on the next test to get a B for the term? Write an inequality to solve

Show your work.

Solution:

5 Because he has to drive on his job, Jaime is paid $0 50 per mile to cover transportation costs In addition, he earns $560 a week His company can’t afford to pay him more than $800 a week, so his paycheck must be less than $800 Which of the following numbers of miles meet this requirement? Select all that apply

A 240 C 436

B 435 D 560

You can write an inequality to represent this situation.

When do you use an open dot in the graph of an inequality?

Recall how to find an average.

21 0 1 2 3