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Main Idea/Vocabulary Write and graph inequalities.

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Example 1 Write Inequalities with SPORTS Members of the little league team must be under 14 years old. Write an inequality for the sentence. Let a = person’s age. Answer: a < 14

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1.A 2.B 3.C 4.D Example 1 A.a < 10 B.a ≤ 10 C.a > 10 D.a ≥ 10 SPORTS Members of the peewee football team must be under 10 years old. Write an inequality for the sentence.

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Example 2 Write Inequalities with CONSTRUCTION The ladder must be over 30 feet tall to reach the top of the building. Write an inequality for the sentence. Let h = ladder’s height. Answer: h > 30

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1.A 2.B 3.C 4.D Example 2 A.h < 300 B.h ≤ 300 C.h > 300 D.h ≥ 300 CONSTRUCTION The new building must be over 300 feet tall. Write an inequality for the sentence.

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Example 3 Write Inequalities with ≤ or ≥ POLITICS The president of the United States must be at least 35. Write an inequality for the sentence. Let a = president’s age. Answer: a ≥ 35

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1.A 2.B 3.C 4.D Example 3 A.a > 18 B.a ≥ 18 C.a < 18 D.a ≤ 18 POLITICS To vote, you must be at least 18 years old. Write an inequality for the sentence.

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Example 4 CAPACITY A theater can hold a maximum of 300 people. Write an inequality for the sentence. Let p = theater’s capacity. Answer: p ≤ 300 Write Inequalities with ≤ or ≥

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1.A 2.B 3.C 4.D Example 4 A.p < 10,000 B.p ≤ 10,000 C.p > 10,000 D.p ≥ 10,000 CAPACITY A football stadium can hold a maximum of 10,000 people. Write an inequality for the sentence.

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Example 5 Determine the Truth of an Inequality For the given value, state whether the inequality is true or false. x – 4 < 6; x = 0 Answer: Since –4 is less than 6, –4 < 6 is true. –4 < 6Simplify 0 – 4 < 6Replace x with 0. ? x – 4 < 6Write the inequality.

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1.A 2.B Example 5 For the given value, state whether the inequality is true or false. x – 5 < 8; x = 16 A.true B.false

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Example 6 Determine the Truth of an Inequality For the given value, state whether the inequality is true or false. 3x ≥ 4; x = 1 Answer: Since 3 is not greater than or equal to 4, the sentence is false. 3x≥ 4Write the inequality. 3(1)≥ 4Replace x with 1. ? 3≥ 4Simplify.

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1.A 2.B Example 6 A.true B.false For the given value, state whether the inequality is true or false. 2x ≥ 9; x = 5

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Example 7 Graph an Inequality Graph n ≤ –1 on a number line. Place a closed circle at –1. Then draw a line and an arrow to the left. Answer:

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1.A 2.B 3.C 4.D Example 7 Graph n ≤ –3 on a number line. A. B. C. D.

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Example 8 Graph an Inequality Graph n > –1 on a number line. Answer: Place an open circle at –1. Then draw a line and an arrow to the right.

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1.A 2.B 3.C 4.D Example 8 Graph n > –3 on a number line. A. B. C. D.

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1.A 2.B 3.C 4.D Five Minute Check 1 A.25 and 27 B.57 and 59 C.157 and 159 D.1,681 and 1,682 Solve using the guess and check strategy. The product of two consecutive odd integers is 3,363. What are the integers? (over Lesson 8-5)

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1.A 2.B 3.C 4.D Five Minute Check 2 A.2 keychains, 4 cups, 3 pens B.4 keychains, 3 cups, 2 pens C.3 keychains, 4 cups, 2 pens D.3 keychains, 2 cups, 4 pens Solve using the guess and check strategy. Jorge decided to buy a souvenir keychain for $2.25, a cup for $2.95, or a pen for $1.75 for each of his 9 friends. If he spent $22.05 on these souvenirs and bought at least one of each type of souvenir, how many of each did he buy? (over Lesson 8-5)

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1.A 2.B 3.C 4.D Five Minute Check 3 A.27 B.31 C.29 D.25 Solve using the guess and check strategy. A number squared is 729. Find the number. (over Lesson 8-5)

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1.A 2.B 3.C 4.D Five Minute Check 4 A.5 quarters, 5 dimes, 9 nickels B.7 quarters, 9 dimes, 3 nickels C.2 quarters, 13 dimes, 4 nickels D.6 quarters, 3 dimes, 10 nickels Solve using the guess and check strategy. Candace has $2.30 in quarters, dimes, and nickels in her change purse. If she has a total of 19 coins, how many of each coin does she have? (over Lesson 8-5)

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1.A 2.B 3.C 4.D Five Minute Check 5 A.4 people B.5 people C.6 people D.7 people In the Brown home, there are 30 total legs on people and pets. Each dog and cat has 4 legs, and each family member has 2 legs. The number of pets is the same as the number of family members. How many people are in the Brown family home? Solve using the guess and check strategy. (over Lesson 8-5)

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