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©Curriculum Associates, LLC Copying is not permitted. 215Lesson 20 Solve Inequalities

Name:Solve Inequalities

Lesson 20

Prerequisite: Solve Equations

Study the example problem showing how to solve an

equation. Then solve problems 1–7.

1What does b represent in the bar model?

2What does each part of the bar model represent?

3Explain how the model shows that 7b 5 91

4What operation will you use to solve the equation

7b 5 91? Solve the equation to find the number of bulbs,

and justify each step you take to solve the equation

Show your work.

Solution:

Example

Taryn planted 91 tulip bulbs in 7 rowsShe planted the

same number of bulbs in each rowHow many bulbs

did she plant in each row?

Create a bar model to represent the 7 rows and the total

number of bulbs that Taryn planted

91

bb b b b b b

©Curriculum Associates, LLC Copying is not permitted.216 Lesson 20 Solve Inequalities

Solve.

5Milo and Audrey sold tickets to the school concert

Milo sold 14 fewer tickets than AudreyIf Milo sold

32 tickets, how many tickets did Audrey sell?

Show your work.

Solution:

6Carmen buys 4 daisies and some roses to make a

flower arrangementThe number of daisies is 1 ·· 3 of the

number of roses that she buysHow many roses does

she buy?

Show your work.

Solution:

7Write a multiplication equation and a subtraction

equation that both involve a fraction and have the

same solutionSolve your equations to show that

the solutions are the same

©Curriculum Associates, LLC Copying is not permitted. 217Lesson 20 Solve Inequalities

Name:

Lesson 20

Write and Solve an Inequality

Study the example problem showing how to write and solve an

inequality for a real-world problem. Then solve problems 1–9.

1Why is the graph in the example shaded to the left?

2Is 2$10 a solution? Substitute 210 into the inequality

in the example to check

3Name an amount that is NOT a solution to the

inequalityExplain how you know

4Suppose the bank sent MrGomez a notice whenever

the amount in his account dropped to $15 or lessHow

would the graph in the example change?

Example

MrGomez gets a notice from the bank when the amount

in his checking account drops below $20For what

amounts will MrGomez receive a notice from the bank?

Use words and symbols to represent the situationLet x

represent the amount in MrGomez’s accountWhen x is

less than $20, the bank will send a notice

x , 20

Graph the inequality to show all of the solutionsUse an

open circle shows that 20 is NOT a solution

025210215220225 5 10 15 20 25

Vocabulary

inequality a statement

that contains the symbol

,, ., #, or $For any

inequality, there are

many possible solutions

These are inequalities

x , 5

x . 22

x # 15

x $ 0

©Curriculum Associates, LLC Copying is not permitted.218 Lesson 20 Solve Inequalities

Solve.

5Write the inequality shown on each graph

a.

222324 21 0 1

b.

210 10 20 30 40230 220250 240 0 50

6The children at Lincoln School go outside for

recess if the temperature is 3°C or higherFor

what temperatures will the students go

outside? Write an inequality to represent this

situationThen graph the solution

7If your score on a computer game is less than 0, you

lose your next turnFor what scores will you lose your

turn? Write an inequality to represent this situation

Then graph the solution

8Write a real-world situation for this inequality: x $ 9

9Explain how an equation and an inequality are

differentGive an example of each

2 4 5 6 70 122 21 3 8

24 0 2 4 628 26212 210 22 8

©Curriculum Associates, LLC Copying is not permitted. 219Lesson 20 Solve Inequalities

Name:

Lesson 20

More Inequalities

Study the example problem showing how to write and

solve an inequality. Then solve problems 1–9.

1Leigh is 40 inches tallCan she ride on the roller coaster?

2Brennon is 38 inches tallCan he ride on the roller

coaster? Use the graph to explain your answer

3Joy wrote the inequality 40 # x to represent the

situationIs her inequality correct?

4Suppose this graph represents a problem about the

height of people riding the roller coasterHow would

the situation have changed?

10 30 40 50 60210 0230 220 20 70

Example

You need to be at least 40 inches tall to ride on the roller

coaster at the amusement parkWhat are some possible

heights for riders? Write an inequality to represent the

heights, and graph the solution on a number line

Use symbols to represent the situationLet x be the

possible heights in inches for riders

x $ 40

Graph the inequality to show all of the solutions

10 30 40 50 60210 0230 220 20 70

©Curriculum Associates, LLC Copying is not permitted.220 Lesson 20 Solve Inequalities

Solve.

Use this situation for problems 5–6.

You must spend at least $10 at the grocery store to get a

free greeting card

5Write an inequality to represent the amount you need

to spend to get a free greeting cardThen graph the

solution on the number line

6If you spend $9 50, will you get a free greeting card?

Use the graph to explain how you know

7Zarina is scuba divingShe will not dive below

230 meters relative to the surface of the waterWrite

an inequality that represents this situationIs 220 a

solution to the inequality? Explain how you know

8Write an inequality that has the solution shown

on the graphThen write a real-world situation for

the inequality

5 7 8 9 103 41 2 6 11

9Markim looks at the graph below and says that 21 is

the only possible negative solutionDo you agree or

disagree? Explain

0 2 3 4 522 2124 23 1 6

12 16 18 20 228 104 6 14 24

©Curriculum Associates, LLC Copying is not permitted. 221Lesson 20 Solve Inequalities

Name:

Lesson 20

Solve Inequalities

Solve the problems.

3The graph shows information about the low

temperature in a particular city in degrees Celsius each

day during one week in JanuaryWrite an inequality

for this situationThen write in words what the graph

shows about the temperature readings

26 24 22 0 6 8 1028210 2 4

2Samuel wants to eat at least 15 grams of protein each

dayLet x represent the amount of protein he should

eat each day to meet his goalWhich inequality

represents this situation?

A x , 15 C x # 15

B x . 15 D x $ 15

Karli chose B as the correct answerHow did she get

that answer?

1Write an inequality for each graph

a.

b.

21 0 12223 2

What does the

direction of the

arrow on the shaded

line tell you about

the inequality?

Would a graph for

this situation have

an open circle or a

closed circle?

What are some

words that describe

a situation in which

the shaded line on

the graph points

left?

10 30 40 50 60210 0230 220 20 70

©Curriculum Associates, LLC Copying is not permitted.222 Lesson 20 Solve Inequalities

6Consider the inequality x . 20 75Tell whether each

statement is True or False

a. 20 75 is a solution to

the inequalityu True u False

b. There are many solutions

to this inequality u True u False

c. All of the solutions to the

inequality are negativeu True u False

d. The inequality 20 75 , x

is equivalent to the given

inequalityu True u False

e. 24 5 is a solution to the

inequalityu True u False

Solve.

4Kalista practices the piano for at least 8 hours each

weekWrite an inequality for this situationThen graph

the solution on the number line

5Which of these values is a solution

to the inequality x 2 1 $ 6?

73 1 ·· 22 510

Show your work.

Solution:

Does a given value

for x make the

inequality true or

false?

How do you know

whether a given

value is a solution to

the inequality?

Does “at least”

include 8 as a

solution?

2 4 6 8 14 16 18022 10 12

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