8-7 Solving Inequalities

Transcription

1 Solve each inequality. Check your solutions. 1. y y z 24 z 3 2. b + 20 > 13 b > < x + ( 3) x > 4 Solve each inequality. Graph each solution on a number line. 4. d d > g g > Isabel earns $50 plus $2.50 for each table she cleans. Write and solve an inequality to find how many tables she must clean to earn at least $ t ; at least 28 tables Solve each inequality. Check your solution. 11. a + 18 < > f f < 4 6. g g q 18 q 2 a < h 12 > 52 h > y y g g p 14 > 12 p > 26 esolutions Manual - Powered by Cognero Page 1

2 16. x < 5 x < n n > z The dance committee has $75 to spend on centerpieces. They spent $30 on flowers. If each vase costs $3, write and solve an inequality to find how many vases they can buy. 3v ; at most 15 vases Solve each inequality. Graph each solution on a number line x > 36 x > 9 z < c 2.1 c b b < b 26. 7y 49 y n < 8 n > 7 b > 22. t + < 28. 3b b 5 b 4 t < 23. Montel pays a $2 entrance fee and $0.75 every time he plays his favorite video game. If he has $10, write and solve an inequality to find how many video games he can play r r y 10; at most 10 games esolutions Manual - Powered by Cognero Page 2

3 k a 31. y > 63 y > Khadijah has at most three hours to work on a math assignment and a history project. If the math assignment will take hour, how much time can Khadijah spend working on her history project? 32. m at most h or 2 h 15 min 33. b b d 6 9 d The 2008 attendance at the Ohio State Fair was at least 16,700 less than the attendance in If the attendance in 2008 was 809,300, write and solve an inequality to find the 2009 attendance. 809,300 x 16,700; x 826,000 Solve each inequality. Check your solutions. 39. a 3.5 < a < b b c 35. c c d > 40 d < 28 esolutions Manual - Powered by Cognero Page 3

4 r r f 8 < 1.1 f < t t y 47. y 28.8 g Write an inequality to represent each situation. Then solve each inequality. 48. Seven more than a number is at most n 24; n The quotient of a number and 3 is greater than the quotient of 5 and 6. > ; n < is at least the product of 6 and a number. 18 6n ; n The difference of a number and 15 is no more than 8. n 15 8 ; n Twelve less than a number is at most 20. n ; n is at least the product of 7 and a number. 28 7n; n Financial Literacy Brian is saving money to buy a new mountain bike. The bike that he likes costs $375.95, and he has already saved $ Write and solve an inequality to find the amount he must still save. x ; at least $ Multiple Representations Consider the inequalities b 4 and b 13. a. Graph Graph each inequality on the same number line. b. Words Do the solution sets of the two inequalities overlap? If so, what does this overlapping area represent? c. Symbols A compound inequality is an inequality that combines two inequalities. Write a compound inequality for the situation. d. Graph Look back at the graph of the solutions for both inequalities. Make another graph that shows only the solution of the compound inequality. a. b. Yes it represents the solutions that satisfy both inequalities. c. 4 b 13 d. esolutions Manual - Powered by Cognero Page 4

5 Graph each compound inequality on a number line < n < Persevere with Problems Write an inequality for the following sentence. The quotient of a number and 5 increased by 4 is at most 8. Name three numbers that are possible solutions. Explain m > g < Use the body temperature scale shown ; x 20; Sample answers: 18, 0, 18 because they are greater than Model with Mathematics Write a real-world problem involving an inequality and negative numbers where the inequality symbol would not be reversed when finding the solution. Sample answer: x + ( 3.60) 15.00; x After a discount of $3.60 was applied to an item, the new price was at most $15. Find the original price of the item. 62. Persevere with Problems Twenty more than half a number is at least 45. Find the least number that meets this condition. a. Suppose Malia has a temperature of 99.2º. Write and solve an inequality to find how much her temperature must increase before she is considered to have a high fever. b. Hypothermia occurs when a person s body temperature falls below 95ºF. Write and solve an inequality that describes how much lower the body temperature of a person with hypothermia will be than a person with a normal body temperature of 98.6ºF. a t > 101; t > 1.8; more than 1.8 F higher b t < 95; t > 3.6; more than 3.6 F lower Use a Counterexample Is the following statement true or false? If false, provide a counterexample. For all values of x, two times x is greater than x. false; If x = 2, then 2x = 4, 2 > Justify Conclusions Is it always, sometimes, or never true that if x y, then y > x? Explain your reasoning to a classmate. Sometimes; If x = 21 and y = 21, then x y is true, but y > x is not true. esolutions Manual - Powered by Cognero Page 5

6 65. Building on the Essential Question Explain how to solve inequalities that involve multiplication and division. Sample answer: To solve an inequality involving multiplication, divide each side by the same number. To solve an equality involving division, multiply each side by same number. If the number is positive, keep the inequality symbol. If the number is negative, reverse the symbol. 66. The length of the rectangle is greater than its width. Which inequality represents the possible values of x? 68. The solutions for which inequality are represented by the following graph? A < 5 B 5 C > 5 A x 17 B x < 17 C x 17 D x > 17 D 5 B 67. If n + 15 > 4, then n could be which of the following values? F 13 G 12 H 11 J 10 J D 69. The product of a number n and four is at most thirty. Which inequality represents the possible values of n? F G H n 120 J n 120 F Write an inequality for each sentence. 70. Leticia made at least $45 babysitting last weekend. l 45 esolutions Manual - Powered by Cognero Page 6

7 71. Marc could pay no more than $8500 for his car. c Adrienne needs an 86% or better to get a B in the class. b 86% 73. There are fewer than 625 students at Everett Middle School. s < The car s tank contains no less than 8.5 gallons of gasoline. g Tyrell has more than 200 foreign coins in his collection. c > 200 Solve each equation. Check your solutions x + 1 = = p h + 5 = 6h d 13 = d n 14 = 3n g + 12 = 3g y + 5 = 5y 5 + 2y t = 2t x 4 = h + 6 = n + 3 = = 4d esolutions Manual - Powered by Cognero Page 7

8 88. A standard showerhead uses about 6 gallons of water per minute. The table shows the relationship between time in minutes and the number of gallons of water used. a. Given m, the number of minutes, write an equation that can be used to find g, the number of gallons used. b. How many minutes elapsed if 72 gallons of water were used? a. g = 6m b. 12 minutes esolutions Manual - Powered by Cognero Page 8