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Mid-Chapter Quiz Solve each inequality. Then graph it on a number line. x 8>4 The solution set is {x | x > 12}. m The solution set is {m | m p 4}. 4< 7 The solution set is {p | p < 3}. t 9 The solution set is {t | t 21}. Lupe s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket. a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is eSolutions Manual - Powered by Cognero Page 1 The solution set is {t | t Mid-Chapter Quiz 21}. Lupe s allowance for the month is $60. She wants to go to a concert for which a ticket costs $45. Write and solve an inequality that shows how much money she can spend that month after buying a concert ticket. She spends $9.99 on music downloads and $2 on lunch in the cafeteria. Write and solve an inequality that shows how much she can spend after these purchases and the concert ticket. a. Let m be the amount Lupe can spend after buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is Lupe can spend $15 after buying a concert ticket. b. Let m be the amount Lupe can spend after downloading music, buying lunch, and buying a concert ticket. Write an inequality. Because she can spend at most $60, the inequality symbol is Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket. Define a variable, write an inequality, and solve each problem. Check your solution. The sum of a number and 2 is no more than 6. Sample answer: Let x = the number. The word sum means addition, and the phrase no more than means the same as less than or equal to. The solution set is {x | x 8}. Check the endpoint with 8 and the direction with a value less than 8. eSolutions Manual - Powered by Cognero Page 2 Mid-Chapter Quiz Lupe can spend $3.01 after downloading music, buying lunch, and buying a concert ticket. Define a variable, write an inequality, and solve each problem. Check your solution. The sum of a number and 2 is no more than 6. Sample answer: Let x = the number. The word sum means addition, and the phrase no more than means the same as less than or equal to. The solution set is {x | x 8}. Check the endpoint with 8 and the direction with a value less than 8. A number decreased by 4 is more than 1. Sample answer: Let x = the number. The phrase decreased by means subtraction, and the phrase more than means greater than. The solution set is {x | x > 3}. Check the endpoint with 3 and the direction with a value greater than 3. Twice a number increased by 3 is less than the number decreased by 4. eSolutions Manual - Powered by Cognero Sample answer: Let x = the number. The word twice means to multiply by 2, and the phrase decreased by Page 3 Mid-Chapter Quiz Twice a number increased by 3 is less than the number decreased by 4. Sample answer: Let x = the number. The word twice means to multiply by 2, and the phrase decreased by means to subtract. The solution set is {x | x < 7}. Check the endpoint with -7 and the direction with a value less than -7. Jane is saving money to buy a new cell phone that costs no more than $90. So far, she has saved $52. How much more money does Jane need to save? $38 more than $38 no more than $38 at least $38 Let c be the amount Jane still needs to save. Write an inequality. The phrase no more than means the same as less than or equal to. So, Jane needs to save no more than $38. The correct choice is choice C. Solve each inequality. Check your solution. eSolutions Manual - Powered by Cognero Page 4 Mid-Chapter Quiz So, Jane needs to save no more than $38. The correct choice is choice C. Solve each inequality. Check your solution. The solution set is {y | y 15}. To check this answer, substitute a number greater than or equal to 15 into the original inequality. If y = 18, then or 6 5, so the solution checks. 4< The solution set is {c | c > 20}. To check this answer, substitute a number greater than 20 into the original inequality. If c = 25, then the solution checks. 8x > 24 The solution set is {x | x < 3}. To check this answer, substitute a number less than 3 into the original inequality. If x = 4, then 8( 4) or 32 > 24, so the solution checks. 2m 10 The solution set is {m | m 5}. eSolutions Manualthis - Powered by Cognero To check answer, substitute or 12 Page 5 a number less than or equal to 5 into the original inequality. If m = 6, then 2( 6) 10, so the solution checks. The solution set is {x | x < 3}. To check this answer, substitute a number less than 3 into the original inequality. If x = 4, then 8( 4) or 32 > 24, Mid-Chapter Quiz so the solution checks. 2m 10 The solution set is {m | m 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If m = 6, then 2( 6) or 12 10, so the solution checks. < The solution set is . To check this answer, substitute a number less than x = 1, then , so the solution checks. 9a 45 The solution set is {a | a 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then 9(2) or 18 45, so the solution checks. > 3 The Manual solution set is {w | w > 18}. eSolutions - Powered by Cognero To check this answer, substitute a number greater than 18 into the original inequality. If w = 12, then Page 6 2> The solution set is {a | a 5}. To check this answer, substitute a number less than or equal to 5 into the original inequality. If a = 2, then 9(2) or Mid-Chapter Quiz 18 45, so the solution checks. > 3 The solution set is {w | w > 18}. To check this answer, substitute a number greater than 18 into the original inequality. If w = 12, then 2> 3, so the solution checks. < 2 The solution set is {k | k < 14}. To check this answer, substitute a number less than 14 into the original inequality. If k = 21, then 3 < 2, so the solution checks. The world s heaviest flying bird is the great bustard. A male bustard can be up to 4 feet long and weigh up to 40 pounds. Write inequalities to describe the ranges of lengths and weights of male bustards. Male bustards are usually about four times as heavy as females. Write and solve an inequality that describes the range of weights of female bustards. a. Let w be the weight of a male bustard. The phrase up to means the same as less than. Both the length and weight of a bustard must be more than zero. 0< <4 0 < w < 40 b. Let w be the weight of a female bustard. The weight of a male bustard can be represented by 4w. Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find the garden. Page 7 maximum ofbya Cognero side of the eSolutions Manual -length Powered Mid-Chapter Quiz Bill is building a fence around a square garden to keep deer out. He has 60 feet of fencing. Find the maximum length of a side of the garden. Let x be the side length of Bill s square garden. The perimeter of the garden can be represented by 4x. Because Bill has only 60 feet of fencing, the perimeter must be less than or equal to 60 feet. So, the garden can be at most 15 feet on each side. Solve each inequality. Check your solution. 4a 2 > 14 The solution set is {a | a > 4}. To check this answer, substitute a number greater than 4 into the original inequality. Let a = 5. So, the solution checks. 2x x 10 eSolutions Manual - Powered by Cognero Page 8 Mid-Chapter Quiz checks. So, the solution 2x x 10 The solution set is {x | x 7}. To check this answer, substitute a number greater than or equal to 7 into the original inequality. Let x = 10. So, the solution checks. p +4< 9 The solution set is {p | p > 13}. To check this answer, substitute a number greater than 13 into the original inequality. Let p = 15. So, the solution checks. 3 eSolutions Manual - Powered by Cognero Page 9 Mid-Chapter Quiz So, the solution checks. 3 The solution set is {d | d 16}. To check this answer, substitute a number greater than or equal to 16 into the original inequality. Let d = 12. So, the solution checks. 2(4b + 1) < 3b + 8 The solution set is {b | b > 2}. To check this answer, substitute a number greater than 2 into the original inequality. Let b = 0. eSolutions Manual - Powered by Cognero So, the solution checks. Page 10 Mid-Chapter Quiz So, the solution checks. 2(4b + 1) < 3b + 8 The solution set is {b | b > 2}. To check this answer, substitute a number greater than 2 into the original inequality. Let b = 0. So, the solution checks. Define a variable, write an inequality, and solve each problem. Check your solution. Three times a number increased by 8 is no more than the number decreased by 4. Sample answer: Let x = the number. Times means multiplication, increased by means addition, no more than means less than or equal to, and decreased by means subtraction. The solution set is {x | x 6}. To check this answer, substitute a number less than or equal to 6 into the original inequality. Let x = 7. eSolutions Manual - Powered by Cognero So, the solution checks. Page 11 Mid-Chapter Quiz So, the solution checks. Define a variable, write an inequality, and solve each problem. Check your solution. Three times a number increased by 8 is no more than the number decreased by 4. Sample answer: Let x = the number. Times means multiplication, increased by means addition, no more than means less than or equal to, and decreased by means subtraction. The solution set is {x | x 6}. To check this answer, substitute a number less than or equal to 6 into the original inequality. Let x = 7. So, the solution checks. Two thirds of a number plus 5 is greater than 17. Sample answer: Let x = the number. Of means multiplication. The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21. eSolutions Manual - Powered by Cognero Page 12 Mid-Chapter Quiz checks. So, the solution Two thirds of a number plus 5 is greater than 17. Sample answer: Let x = the number. Of means multiplication. The solution set is {x | x > 18}. To check this answer, substitute a number greater than 18 into the original inequality. Let x = 21. So, the solution checks. Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? 2 3 4 5 Let g be the number of games Kyle bowls. The solution set is eSolutions Manual - Powered by Cognero . Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H. Page 13 Mid-Chapter Quiz So, the solution checks. Shoe rental costs $2, and each game bowled costs $3. How many games can Kyle bowl without spending more than $15? 2 3 4 5 Let g be the number of games Kyle bowls. The solution set is . Because Kyle cannot bowl one-third of a game, the most games he can bowl is 4. So, the correct choice is H. eSolutions Manual - Powered by Cognero Page 14