Math Assignment

©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.

1 What does b represent in the bar model?

2 What does each part of the bar model represent?

3 Explain how the model shows that 7b 5 91

4 What 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 rows She planted the same number of bulbs in each row How 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.

5 Milo and Audrey sold tickets to the school concert Milo sold 14 fewer tickets than Audrey If Milo sold 32 tickets, how many tickets did Audrey sell?

Show your work.

Solution:

6 Carmen buys 4 daisies and some roses to make a

flower arrangement The number of daisies is 1 ·· 3 of the

number of roses that she buys How many roses does

she buy?

Show your work.

Solution:

7 Write a multiplication equation and a subtraction equation that both involve a fraction and have the same solution Solve 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.

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

2 Is 2$10 a solution? Substitute 210 into the inequality in the example to check

3 Name an amount that is NOT a solution to the inequality Explain how you know

4 Suppose the bank sent Mr Gomez a notice whenever the amount in his account dropped to $15 or less How would the graph in the example change?

Example

Mr Gomez gets a notice from the bank when the amount in his checking account drops below $20 For what amounts will Mr Gomez receive a notice from the bank?

Use words and symbols to represent the situation Let x represent the amount in Mr Gomez’s account When x is less than $20, the bank will send a notice

x , 20

Graph the inequality to show all of the solutions Use 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.

5 Write the inequality shown on each graph

a. 222324 21 0 1

b. 210 10 20 30 40230 220250 240 0 50

6 The children at Lincoln School go outside for recess if the temperature is 3°C or higher For what temperatures will the students go outside? Write an inequality to represent this situation Then graph the solution

7 If your score on a computer game is less than 0, you lose your next turn For what scores will you lose your turn? Write an inequality to represent this situation Then graph the solution

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

9 Explain how an equation and an inequality are different Give 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.

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

2 Brennon is 38 inches tall Can he ride on the roller coaster? Use the graph to explain your answer

3 Joy wrote the inequality 40 # x to represent the situation Is her inequality correct?

4 Suppose this graph represents a problem about the height of people riding the roller coaster How 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 park What 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 situation Let 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

5 Write an inequality to represent the amount you need to spend to get a free greeting card Then graph the solution on the number line

6 If you spend $9 50, will you get a free greeting card? Use the graph to explain how you know

7 Zarina is scuba diving She will not dive below 230 meters relative to the surface of the water Write an inequality that represents this situation Is 220 a solution to the inequality? Explain how you know

8 Write an inequality that has the solution shown on the graph Then write a real-world situation for the inequality

5 7 8 9 103 41 2 6 11

9 Markim looks at the graph below and says that 21 is the only possible negative solution Do 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.

3 The graph shows information about the low temperature in a particular city in degrees Celsius each day during one week in January Write an inequality for this situation Then write in words what the graph shows about the temperature readings

26 24 22 0 6 8 1028210 2 4

2 Samuel wants to eat at least 15 grams of protein each day Let x represent the amount of protein he should eat each day to meet his goal Which inequality represents this situation?

A x , 15 C x # 15

B x . 15 D x $ 15

Karli chose B as the correct answer How did she get that answer?

1 Write 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

6 Consider the inequality x . 20 75 Tell whether each statement is True or False

a. 20 75 is a solution to the inequality u True u False

b. There are many solutions to this inequality u True u False

c. All of the solutions to the inequality are negative u True u False

d. The inequality 20 75 , x is equivalent to the given inequality u True u False

e. 24 5 is a solution to the inequality u True u False

Solve.

4 Kalista practices the piano for at least 8 hours each week Write an inequality for this situation Then graph the solution on the number line

5 Which of these values is a solution to the inequality x 2 1 $ 6?

7 3 1 ·· 2 2 5 10

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