For each of the following situations define a variable and write an inequality or a compound inequality to describe it and then, graph them.

Transcription

1 ACTIVITY I The Math Translator For each of the following situations define a variable and write an inequality or a compound inequality to describe it and then, graph them. 1. You have to be at most 12 years old to eat off the kid s menu. 2. Speed limits show the fastest speed you may drive under good conditions, but you can be issued a ticket for driving too slowly. When the posted speed limit is 70 mph, the minimum speed limit is 50 mph. For each of the following situations define a variable and write an inequality or a compound inequality to describe it and then, graph them. 1. Busch Gardens hosts one of the world s top roller coasters, the legendary Kumba. To the discontent of many tourists, Kumba has a height restriction of at least According the Kelly Blue Book a fair price for a 2010 Hummer H3T is at least $30, but no more than $31, For each of the following situations define a variable and write an inequality or a compound inequality to describe it and then, graph them. 1. To be able to use a booster sit, a child must weigh at least 40 pounds and no more than 80 pounds. 2. The minimum age established by law in order to vote in a public election is 18 years old For each of the following situations define a variable and write an inequality or a compound inequality to describe it and then, graph them. 1. The greatest weight that a forklift can raise is 2500 pounds. 2. The highest recorded temperature in Florida was 109 F on June 29, The lowest recorded temperature was 2 F on February 13, Curriculum and Instruction, Mathematics Page 3 of 11

2 For each of the following situations define a variable and write an inequality or a compound inequality to describe it and then, graph them. 1. The minimum wage in Florida is $7.25 per hour. 2. At an auction, the lowest bid for an item was $25. The highest bid for the same item was $64. For each of the following situations define a variable and write an inequality or a compound inequality to describe it and then, graph them. 1. Each class in our school has no more than 25 students. 2. The credit score is used to predict consumers' ability to repay debt. Credit scores range from 300 up to 850. Curriculum and Instruction, Mathematics Page 4 of 11

3 ACTIVITY II PRACTICE YOUR SKILLS Solve each inequality. Graph the solution. 1. 6p p 2. 3x 7 > (s + 1) < 2s (12x + 1) (x + 3) Solve each compound inequality. Graph the solution < 2x + 3 < a - 4 > 16 or 3a + 2 < (3x + 5) < > m or -2m < -14 Curriculum and Instruction, Mathematics Page 5 of 11

4 ACTIVITY III Inequalities in my World REASON AND APPLY 1. SPORTS. A light heavyweight boxer enrolls in an exercise program that guarantees a loss of at least 2 pounds per week. The boxer s weight at the beginning of the program is 214 pounds and he would like to find the maximum number of weeks before he attains his goal weight of 175 pounds. 2. CONSTRUCTION. The cost to rent a construction crane is $750 per day plus $250 per hour of use. What is the maximum number of hours the crane can be used each day if the total cost is not to exceed $2, per day? 3. DAILY SALES. A doughnut shop sells a dozen doughnuts for $2.95. Beyond the fixed costs (rent, utilities, and insurance) of $150 per day, it costs $1.45 for enough materials (flour, sugar, and so on) and labor to produce a dozen doughnuts. The daily profit from doughnut sales varies between $50 and $200. Between what levels (in dozens) do the daily sales vary? 4. HORSE RIDING: The height of a horse is measured in a vertical line from the ground to the withers (at the base of the neck). Horses are measured in "hands" where one hand = 4 inches. If a horse is more than an exact number of hands high (hh), the extra inches are given after a decimal point, e.g. 14 hands 2 inches is written as 14.2 hh. Normal riding horses are between 14.3 hh and 17 hh, inclusive. Horses shorter than 14.3 hands are called ponies and horses over 17 hh are often called draft (or work) horses. Write an inequality statement stating the heights, in inches, of equines (horses) that do not fit the normal riding horse height specifications. 5. SCHOOL: The range of scores for a B grade on the last math quiz was 17 to 15 inclusive. a) If Tom s score was at most 2 less than twice Kasha s score of 6, did he earn a grade of B? b) What is the lowest score Kasha could make for Tom to get a B grade on the quiz? Curriculum and Instruction, Mathematics Page 6 of 11

5 ACTIVITY IV ASSESSING YOUR KNOWLEDGE I. Write a short paragraph describing an example of a real-world situation that involves a compound inequality. Solve and graph the solution, and explain how you arrived at your answer. II. Determine which value of x is a solution of the inequality 1. 5x 12 > 0 A. x = 3 B. x = -3 C. x = D. x = < < 2 F. x =0 G. x = -5 H. x = 1 I. x = 3. Which of the following expressions is represented by the graph shown below? A. -3 < x < -1 B. x < -3 or x > -1 C. -3 < x -1 D. x < -3 or x -1 Curriculum and Instruction, Mathematics Page 7 of 11

6 4. Which expression has the entire number line as its graphs? F. x 0 G. x 0 H. 5 < x < 10 I. x > 5 or x Ana earns $5.95 per hour working after school. She needs at least $215 for her holiday shopping. How many hours must she work to reach her goal? A. At least 37 hours B. At least 35 hours C. At least 36 hours D. At least 38 hours Curriculum and Instruction, Mathematics Page 8 of 11