Name ________________________________ Date __________________ Class _________________

Practice A Inequalities

Graph the solutions of each inequality on a number line. 1. x > 2 2. b < –1

3. m ≥ 4 4. p < 3

Solve and graph each inequality. 5. y + 3 > 7 6. r − 7 ≥ 1

_______________________________________ ________________________________________

7. 4q ≤ 20 8. 2z < 2

_______________________________________ ________________________________________

LESSON 13-5

Name ________________________________ Date __________________ Class _________________

Practice B Inequalities

Graph the solutions of each inequality on a number line. 1. c ≥ −6 2. w ≤ 5

Solve and graph each inequality. 3. j − 4 ≤ 1 4. h + 7 > 9

_______________________________________ ________________________________________

5. 5g ≥ 15 6. 2f ≤ 4

_______________________________________ ________________________________________

Write an inequality for each sentence. Then graph your inequality on a number line. 7. k is greater than or equal to seven. 8. a plus one is less than five.

_______________________________________ ________________________________________

9. A soccer team scored 8 goals in its last game. This was the highest number of goals scored all year. Let g represent the number of goals scored in the other games. Write an inequality relating g to the number of goals scored last game.

_______________________________________

LESSON 13-5

Name ________________________________ Date __________________ Class _________________

Practice C Inequalities

Graph the solutions of each inequality on a number line.

1. d ≤ 3 2. s > − 12

Solve and graph each inequality. 3. n − 6 < −8.5 4. x + 2 ≤ −3

_______________________________________ ________________________________________

5. 4r < –1 6. 3t ≤ 18

_______________________________________ ________________________________________

Write an inequality for each sentence. Then graph your inequality on a number line. 7. c minus two is less than or equal to one. 8. b plus three is greater than four.

_______________________________________ ________________________________________

9. An amusement park ride has a restriction on height that says “You must be at least 60 inches tall to ride.” Let h represent the height of any person that can ride. Write an inequality relating h to the minimum height of a person that can ride this ride.

_______________________________________

LESSON 13-5

Name ________________________________ Date __________________ Class _________________

Review for Mastery Inequalities

An inequality is a statement that two expressions are not equal. For inequalities with a variable, any value of the variable that makes the inequality statement true is a solution of the inequality.

Inequalities are written using the symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). When graphing the solution to an inequality, use an empty circle for < or >, and a solid circle for ≤ or ≥. You use inverse operations to solve inequalities. This should be familiar since you use inverse operations to solve equations, too.

Solve the inequality 4x ≤ 12. 4x ≤ 12

4x4≤

124

Divide both sides of the inequality by 4.

x ≤ 3 x is less than or equal to 3.

To graph the solutions, place a solid circle at 3 and shade to the left.

Graph each inequality. 1. x > 4 2. x ≤ 1

Solve and graph each inequality. 3. x + 2 ≥ 6 4. 5x ≥ 20

____________________________________________ ________________________________________

LESSON 13-5

Name ________________________________ Date __________________ Class _________________

Challenge Compound Inequalities

A compound inequality combines two inequalities by the word and or the word or. The compound inequality x ≥ −2 and x < 4 can be written as −2 ≤ x < 4. The graph of this inequality is shown below.

The graph of the compound inequality 2or 3x x< − > is shown, too.

Graph each compound inequality. 1. −3 < x ≤ 1 2. x ≤ −1 or x > 5

Solve and graph each compound inequality. 3. −1 < 2x + 3 < 11 4. x + 3 < 1 or 2x > 6

_______________________________________ ________________________________________

5. 3x ≤ −3 or x − 1 > 4 6. −10 ≤ 2x − 6 < 2

_______________________________________ ________________________________________

LESSON 13-5

Name ________________________________ Date __________________ Class _________________

Problem Solving Inequalities

Write an inequality for each sentence. Then graph your inequality on the number line. 1. A sign on a roller coaster states you must be

48 inches or taller to ride. Let h represent the height of a person who can ride this ride.

___________________________

2. Tony is able to trade the tickets he won for a prize that is valued at 300 tickets or less. Let t represent the number of tickets the prize costs.

___________________________

3. Rosella bought some flowers that will only bloom when the air temperature is greater than 62°. Let a represent the air temperature when the flowers bloom.

___________________________

Solve each problem. Choose the letter of the best answer. 4. A basketball team scored at least

43 points in each game last season. Let s represent the number of points the team scored each game. Which inequality represents this situation? A s > 43 C s ≥ 43 B s < 43 D s ≤ 43

6. The room temperature in an office

was 70 or less each day the office was open. Let t represent the temperature of the office each day. Which inequality represents this situation? A t > 70 C t ≥ 70 B t < 70 D t ≤ 70

5. A widget must weigh less than 24 ounces to pass quality control. Let w be the weight of a widget manufactured at a plant. Which inequality represents this situation? F w > 24 H w ≥ 24 G w < 24 J w ≤ 24

7. It is recommended that students

spend more than 30 minutes on homework each night. Let x represent the number of minutes a student spends on homework each night. Which inequality represents this situation? F x > 30 H x ≥ 30 G x < 30 J x ≤ 30

LESSON 13-5

Name ________________________________ Date __________________ Class _________________

Reading Strategies Understand Symbols

An inequality states that two quantities are not equal. The table lists the words and symbols that are used to show inequalities. Symbol < > ≤ ≥ Words Less than

Fewer than Below

Greater than More than Above

Less than or equal to At most No more than

Greater than or equal to At least Not less than

You can use the table to translate words into symbols.

Example: The number of students in the class is greater than 25.

Let s be the number of students in the class.

The number of students in the class is greater than 25.

s > 25 The inequality is s > 25.

Tell which symbol you use for each situation.

1. The number of books on the shelf is less than 14. __________________________

2. The number of pennies in the jar is at least 50. __________________________

3. The number of apples in the bowl is at most 8. __________________________

4. The temperature is no more than 75°. __________________________

Draw a line to match each sensitive with the correct inequality.

5. The number of birds in the cage is less than 10. x ≥ 10

6. The number of girls in the class is at least 10. x ≤ 10

7. There are more than 10 pictures on the wall. x > 10

8. There are no more than 10 CDs in the box. x < 10

LESSON 13-5

Find the words “greater than” in the table.

Replace the words with the correct symbol.

Name ________________________________ Date __________________ Class _________________

Puzzles, Twisters & Teasers Build a Solution

Solve each inequality. On the lines below, write the variable, the Inequality Code, and the Solution Code to form a three-letter word. Note that when multiplying or dividing an inequality by a negative number, you must reverse the inequality symbol: −2x < 12 becomes x > −6 when divided by −2.

Inequality Codes Solution Codes

< A −2 B

≤ E 5 D

≥ I 2 G

> O −4 N

−6 T

1. d + 12 > 14

_________________ _________________ _________________

2. 2p < −2

_________________ _________________ _________________

3. −5t > 10

_________________ _________________ _________________

4. b − 15 ≤ −10

_________________ _________________ _________________

5. −k ≤ 6

_________________ _________________ _________________

LESSON 13-5

Name ________________________________ Date __________________ Class _________________

CODE

61305 Answers

LESSON 13-5

Practice A 1.

2.

3.

4.

5. y > 4

6. r ≥ 8

7. q ≤ 5

8. z < 4

Practice B 1.

2.

3. j ≤ 5

4. h > 2

5. g ≥ 3

6. f ≤ 8

7. k ≥ 7

8. a < 4

9. g ≤ 8

Practice C 1.

2.

3. n < −2.5

4. x ≤ −5

5. r < −4

6. t ≤ 6

7. c ≤ 3

8. b > 1

9. h ≥ 60

Review for Mastery 1.

2.

3. x ≥ 4

4. x > 4

Challenge 1.

2.

3. −2 < x < 4

4. x < −2 or x > 3

5. x ≤ −1 or x > 5

6. −2 ≤ x < 4

Problem Solving 1. h ≥ 48

2. t ≤ 300

3. a > 62

4. C 5. G 6. D 7. F

Reading Strategies 1. < 2. ≥ 3. ≤ 4. ≤ 5. x < 10 6. x ≥10 7. x > 10 8. x ≤10

Puzzles, Twisters & Teasers 1. DOG 2. PAN 3. TAB 4. BED 5. KIT