The solution set is {n n < 60}.
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1 The Jefferson Band Boosters raised more than $5500 from sales of their $15 band DVD. Define a variable, and write an inequality to represent the number of DVDs they sold. Solve the inequality and interpret your solution. Let d = the number of DVDs sold. This means that the band sold at least 367 DVDs. Solve each inequality. Graph the solution on a number line. The solution set is {n n < 60}. The solution set is {r r esolutions Manual - Powered by Cognero Page 1
2 The solution set is {c 42}. The solution set is {h h < 10}. 9t > 108 The solution set is {t t > 12}. 84 < 7 esolutions Manual - Powered by Cognero Page 2
3 84 < 7v The solution set is {v v > 12}. 6x The solution set is. 5z The solution set is {z 8}. esolutions Manual - Powered by Cognero Page 3
4 Define a variable, write an inequality, and solve each problem. Then interpret your solution. Mario purchases a prepaid phone plan for $50 at $0.13 per minute. How many minutes can Mario talk on this plan? Let m = the number of minutes that Mario can talk. So, Mario can talk up to 384 minutes. Rodrigo needs at least $560 to pay for his spring break expenses, and he is saving $25 from each of his weekly paychecks. How long will it be before he can pay for his trip? Let p = the number of pay periods for which Rodrigo will need to save. So, Rodrigo will need to save for 23 weeks. Solve each inequality. Graph the solution on a number line. The solution set is {m 68}. esolutions Manual - Powered by Cognero Page 4
5 The solution set is {a a < 40}. The solution set is {c c > 121}. The solution set is {d 68}. esolutions Manual - Powered by Cognero Page 5
6 The solution set is {x 20}. The solution set is {f f < 432}. The solution set is {h h >21}. esolutions Manual - Powered by Cognero Page 6
7 The solution set is {j 16}. The solution set is {n 108}. 6p The solution set is {p 16} esolutions Manual - Powered by Cognero Page 7
8 4r < 64 The solution set is {r r < 16}. 32 > 2y The solution set is {y y > 16}. 26 < 26t The solution set is {t t > 1}. 6v > 72 The solution set is {v v < 12}. esolutions Manual - Powered by Cognero Page 8
9 3z The solution set is {z 11}. 4b 3 The solution set is. 2d < 5 The solution set is. 7 > 5 esolutions Manual - Powered by Cognero Page 9
10 7f > 5 The solution set is. To remain on the cheerleading squad, Lakita must attend at least of the study table sessions offered. She attends 15 sessions. If Lakita met the requirements, what is the maximum number of study table sessions? Let s represent the number of sessions. At most, 25 study table sessions are offered. How many bracelets can Caitlin buy for herself and her friends if she wants to spend no more than $22? Let b represent the number of bracelets. Caitlin can buy no more than 4 bracelets. esolutions Manual - Powered by Cognero Page 10
11 The National Honor Society at Pleasantville High School wants to raise at least $500 for a local charity. Each student earns $0.50 for every quarter of a mile walked in a walk-a-thon. How many miles will the students need to walk? Let m represent the number of quarter miles. The students needs to walk at least 1000 quarter miles or at least 250 miles. The American history classes are planning a trip to a local museum. Admission is $8 per person. Determine how many people can go for $260. Let p represent the number of people. No more than 32 people can go to the museum. If gasoline costs $3.15 per gallon, how many gallons of gasoline, to the nearest tenth, can Jan buy for $24? Let g represent the number of gallons of gasoline. Jan can buy no more than 7.6 gallons of gasoline. esolutions Manual - Powered by Cognero Page 11
12 Match each inequality to the graph of its solution. a. b. c. d. The point is at 13.5, so the correct choice is b. 25j The point is at 0.32, so the correct choice is a. 3.6p < 4.5 The point is at 1.25, so the correct choice is d. esolutions Manual - Powered by Cognero Page 12
13 2.3 < 5t The point is at 0.46, so the correct choice is c. Fewer than 42 employees at a factory stated that they preferred fudge over fruit candy. This is about two thirds of the employees. How many employees are there? Let e represent the number of employees. So, there are fewer than 63 employees. A certain travel agency employs more than 275 people at all of its branches. Approximately three fifths of all the people are employed at the west branch. How many people work at the west branch? Let p represent the number of people. So, there are more than 165 people employed at the west branch. esolutions Manual - Powered by Cognero Page 13
14 MULTIPLE The equation for the volume of a pyramid is Draw a pyramid with a square base b cm long and a height of h cm. Suppose the pyramid has a volume of 72 cm 3. Write an equation to find the height. Create a table showing the value of h when b = 1, 3, 6, 9, and 12. Write an inequality for the possible lengths of b such that b < h. Write an inequality for the possible lengths of h such that b > h. a. b. c. b h d.b < h when 0 < b < 6; b > h when 6 < h. Taro and Jamie are solving 6d 84. Is either of them correct? Explain your reasoning. Taro is correct. Jamie reversed the inequality sign when dividing by 6. The inequality sign should only be reversed when dividing or multiplying by a negative number. Solve each inequality for. Assume that > 0. esolutions Manual - Powered by Cognero Page 14
15 CHALLENGE Solve each inequality for x. Assume that a > 0. a. b. c. When dividing by a negative number, reverse the inequality symbol. b. c. Determine whether x 2 > 1 and x > 1 are equivalent. Explain. Not equivalent; the inequalities do not have the same solution sets. If x = 2, then x 2 = 4 and 4 > 1. The solution set of x 2 > 1 contains the subsets of real numbers given by xx < 1. esolutions Manual - Powered by Cognero Page 15
16 Explain whether the statement If a > b, then is sometimes, always, or never true. Sometimes. Consider three cases. Case I: a > 0 and b Choose a = 3 and b. Case II: a < 0 and b Choose a = 2 and b = 3. Then 2 > 3, but. Case III: a > 0 and b Choose a = 2 and b = 3. Then 2 > 3, and The statement is only true when a > 0 and b < 0. Create a realworld situation to represent the inequality. Student answers may vary. Sample answer: The temperature never exceeds. How are solving linear inequalities and linear equations similar? different? esolutions Manual - Powered by Cognero Page 16
17 WRITING IN MATH How are solving linear inequalities and linear equations similar? different? Sample answer: The same processes are used when solving linear inequalities and equations that involve addition, subtraction, multiplication, or division by a positive number. However, when a linear inequality is multiplied or divided by a negative number, the inequality symbol must change directions so that the inequality remains true. For example: Inequality: Equation: Juans long-distance phone company charges 9for each minute. Which inequality can be used to find how long he can talk to a friend if he does not want to spend more than $2.50 on the call? m m 0.09m m 2.50 The rate 0.09 is the rate to be multiplied by each minute. So choices A and B can be eliminated. If he does not want to spend more than $2.50, then choice D is correct. esolutions Manual - Powered by Cognero Page 17
18 Find the value of x. Let y represent the height of the smaller triangle. If y = 8, then So, x is 10 inches. What is the greatest rate of decrease of this function? esolutions Manual - Powered by Cognero Page 18
19 What is the greatest rate of decrease of this function? The greatest rate of decrease is when the slope is the steepest and negative. This means that the line will slope down from left to right. So, the steepest line is between ( So, the correct choice is F. What is the value of x if 4x 3 = 2x? 2 2 So, the correct choice is C. esolutions Manual - Powered by Cognero Page 19
20 Solve each inequality. Check your solution, and then graph it on a number line a < 6a {a a > 4} 2y y 7 2b > 12b esolutions Manual - Powered by Cognero Page 20
21 Find the inverse of each function. esolutions Manual - Powered by Cognero Page 21
22 Pam is having blinds installed at her home. The cost c of installation for any number of blinds b can be described by c = b. Graph the equation and determine how much it would cost if Pam has 8 blinds installed. Evaluate c = b for b = 8. So, it would cost Pam $77 to have 8 blinds installed. A boater radioed for a helicopter to pick up a sick crew member. At that time, the boat and helicopter were at the positions shown. How long will it take to reach the boat? Let t represent the time. It should take the helicopter 2 hours to reach the boat. esolutions Manual - Powered by Cognero Page 22
23 Solve each open sentence. x + 3 = 10 Case1: Case2: {13, 7} 2x 8 = 6 Case1: Case2: {1, 7} 3x + 1 = 2 means the distance between 3x and 1 is 2. Since distance cannot be negative, the solution is the empty set. esolutions Manual - Powered by Cognero Page 23
24 Solve each equation. 4y + 11 = 19 2x 7 = 9 + 4x + 2x = 4x 8 esolutions Manual - Powered by Cognero Page 24
25 (6w 3) = 3w + 12 esolutions Manual - Powered by Cognero Page 25
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