Name: _____________________ Date: _______________________

Target D-2 Extra Practice

1. Write a word statement to express the meaning of each inequality.

Inequality Word Statement

a) m > –2

b)

c)

d) m ≥ 2

2. Circle true or false for each of the following statements. If the statement is false, rewrite it to make it true.a) True / False A closed circle indicates that the boundary point is not a

possible value.____________________________________________________________________________________________________________________

b) True / False The inequality –4 < x means x is greater than –4.____________________________________________________________________________________________________________________

c) True / False A boundary point is always shown on a number line using an open circle.____________________________________________________________________________________________________________________

For #3 to #6, fill in the missing information.

Name Date

a) Represent the inequality verbally using a real-life context.b) Represent the inequality graphically.c) Represent the inequality algebraically.

a) Verbally b) Graphically c) Algebraically

Example:The height of a rocket that is launched 1 m below sea level

h ≥ –1, where h is the height of the rocket

3. The temperature below –4 ºC

4. 2 ≥ x

5.

6. x ≥ 0 and x ≤ 5

Extra Practice Answers1. a) m is greater than negative 2.

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Name: _____________________ Date: _______________________

b) A number is less than –2.c) A number is greater than –2 and less than or equal to 2.d) m is greater than or equal to 2.2. a) False. Example: A closed circle indicates that the boundary point is a possible value. b) Truec) False. Example: A boundary point is shown on a number line using either an open circle or a closed circle.3. b)

c) t < –4, where t is the temperature.4. a) Example: The temperature of a town that is never warmer than 2 ºC.b)

5. a) Example: The number of players for a game that requires more than two people to play. c) p > 2, where p is the number of players6. a) Example: The number of people that can fit in a car that seats five.b)

Target D-2 Extra Practice1. List three values that would make each inequality or combination of

inequalities true.a) x ≤ –4 b) x > –3

Name Date

c) x ≥ –2 and x ≤ 52. Solve each inequality.

a) x + 5 ≤ 12 b) 2 > x – 9c) 7.4 + x ≥ 6.2 d) x – 4.2 < 3.5e) 4x ≤ –16 f) –1.3x > 16.9

g) ≤ –4 h) – ≥ 33. Verify if the specified solution is correct for each inequality.

a) 2x < –10; x > –5 b) –3x ≤ –24; x ≤ 8

c) –9 ≥ – x; 3 ≥ x d) ; x < 20e) 2x ≥ –16; x ≥ –8 f) –7 + x > –2; x > –9

4. A balloon company guarantees that at least 18 of the balloons in each package are red. Fifteen percent of the balloons are red. What is the number of balloons in a package?a) Write an inequality to model the situation.b) Solve and verify the inequality.c) Represent your answer verbally and graphically.

5. a) Write and solve an equation to determine the values of x that give the rectangle shown an area of no more than 25 square units.

b) Are there values of x that would not be possible for the length of the rectangle? Explain.

Extra Practice Answers1. a) –4 or any number less than –4. Examples: –4, –5, –6b) Any number greater than –3. Examples: –2, –1, 0c) Any number between –2 and 5, including –2 and 5: –2, –1, 0, 1, 2, 3, 4, or 52. a) x ≤ 7 b) 11 > x or x < 11 c) x ≥ –1.2 d) x < 7.7 e) x ≤ –4 f) x > –13g) x ≤ –20 h) x ≥ –12

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Name: _____________________ Date: _______________________

3. a) x > –5 is not correct. b) x ≤ 8 is correct. c) 3 ≥ x is not correct. d) x < 20 is not correct. e) x ≥ –8 is correct. f) x > –9 is not correct.4. a) 0.15b ≥ 18, where b is the number of balloons in the package.b) b ≥ 120c) The number of balloons in a package is 120 balloons or more.

5. a) 5(x + 2) ≤ 25; x ≤ 3 b) The value of x must be greater than –2 or the length of the rectangle would not exist.

Target D-2 Extra Practice

1. Explain how to verify that the solution to the inequality – 2 ≤ 6 is x ≤ 16.2. Solve each inequality.

a) 3x – 5 > 2x + 4 b) 4x + 3.2 < 2x + 1.4

Name Date

c) x + 8 ≤ (3x – 5) d) 6(5 – x) ≤ 7(x – 5)3. Solve. Draw a number line to represent each solution.

a) 9x + 4 ≤ 5x + 12 b) 5x – 2 > 9x – 10c) 3(2x – 3) < 13 + 2(x – 1) d) 4(2x – 1) – 5(x + 1) ≥ 9

4. Verify each solution.

a) 2x – 9 > 5x + 6; x < –5 b) (x + 3) ≤ 9 + 2(x + 4); x ≤ 5. Your parents are celebrating their 25th wedding anniversary. They have

compared the rates at two banquet halls. Fancy Feast charges $200 for the hall plus $30 per person. Beautiful Banquet charges $400 for the hall plus $20 per person.a) Write an inequality to represent the number of people who could attend

the celebration at Fancy Feast with a cost of no more than $2000.b) How many people need to attend to make Beautiful Banquet more cost

efficient? Show your work.6. The following are the wages for two summer jobs building grain bins.

Job A: $60 per bin plus $120 per day Job B: $75 per bin plus $90 per dayWrite and solve an inequality to determine how many grain bins you would need to build each day to make Job B pay more than Job A.

Extra Practice Answers1. Example: Substitute the boundary point to check that both sides are equal.

– 2 ≤ 6

– 2 ≤ 6 8 – 2 ≤ 6 6 ≤ 6

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Name: _____________________ Date: _______________________

Then, substitute one other number from the solution to determine if it makes the inequality true.

– 2 ≤ 6

– 2 ≤ 6 –3 – 2 ≤ 6 –5 ≤ 6

2. a) x > 9 b) x < –0.9 c) x ≥ d) x ≥ 53. a) x ≤ 2

b) x < 2;

c) x < 5;

d) x ≥ 6;

4. a) x < –5 is correct. b) x ≤ is correct.5. a) 30n + 200 ≤ 2000 or 200 + 30n ≤ 2000, where n is the number of peopleb) 30n + 200 > 20n +400; n > 20If more than 20 people attend, Beautiful Banquet will be more cost efficient.6. Let g represent the number of grain bins you build.75g + 90 > 60g + 120; g > 2Job B pays more than Job A if you build more than two grain bins each day.

Extra Practice 3

Lesson 6.3: Introduction to Linear Inequalities

1. State 3 values of the variable that satisfy each inequality.a) c < 7 b) a≥−3 c) 5 < n d) −1≥ y

2. Write the inequality that is graphed on each number line.

Target D-2

Name Date

a)

b)

c)

d)

3. Write an inequality to describe each situation, then graph it.

a) The gas tank in a car contains no more than 55 L of gas. _________________

b) The minimum age you must be to watch the movie is 13. _________________

Extra Practice 3

Lesson 6.3

1. Answers will vary.a) 6, 0, –2b) –3, 0, 2c) 6, 10, 20d) –1, –5.5, –10

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Name: _____________________ Date: _______________________

2. Variables may differ.a) x ≥ –6b) x < 4c) x > 7.5d) x ≤ –12

3. Variables may differ.a) g ≤ 55

b) a ≥ 13

Name Date

Extra Practice 4

Lesson 6.4: Solving Linear Inequalities by Using Addition and Subtraction

1. Match each inequality with the graph of its solution.a)g+3<9 b) 5≥m−2 c) 2+ y≥−4 d) −1< f +3

i)

ii)

iii)

iv)

2. Solve, then graph each inequality.a)

b)

c)12+ 4

7p>13

10

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Target D-2

Name: _____________________ Date: _______________________

Extra Practice 4

Lesson 6.4

1. a) iib) iiic) id) iv

2. a) t > 4

b) s ≤ 3.5

c) p >

Name Date

Extra Practice 5

Lesson 6.5: Solving Linear Inequalities by Using Multiplication and Division

1. Do not solve each inequality. Determine which of the given numbers are solutions of the inequality.a) 3 t<−5 b) 5−3 d≥2−d

–3, 0, 1 –5, 0, 5

2. Solve each inequality and graph the solution.a) −3 .5 a<−1. 3a+6. 6

b)−5 f

6−2

3> 4

3

c) 1 .3−2. 5 x≤−1 .1 x−0 .52

d) −3 (n−2. 5 )≤4 (3 . 5−n )

3. Nadia gets paid $1000 per month plus 5% commission on her sales. She wants to earn at least $2200 this month. Write an inequality to represent this situation, then solve it to determine how much Nadia must sell to reach her goal.

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Target D-2

Name: ________________________________ Date: ________________________

.…BLM 9–5.…Extra Practice 5

Lesson 6.5

1. a) –3b) –5, 0

2. a) a > –3

b) f < –

c) x ≥ 1.3

d)n ≤ 6.5

3. 1000 + 0.05s ≥ 2200s ≥ 24 000 Nadia must sell at least $24 000 to reach her goal.

Copyright © McGraw-Hill Ryerson, 2009