Write an inequality for the graph. Then, in words, describe all the values of x that make the inequality true
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1 Name Date. Practice A Write an inequality for the graph. Then, in words, describe all the values of that make the inequality true Write the word sentence as an inequality.. A number is at most.. A number y added to is greater than 7.. A number c multiplied by is less than. 6. A number m minus. is no less than. Tell whether the given value is a solution of the inequality. 7. t ; t = w < ; w = 9. p +.6 ; p = 0. d > ; d = 0 Graph the inequality on a number line.. k >. n.. In order to try out for one of the parts in a play at the local theater, you must be at most years old. Write an inequality that represents this situation. Tell whether the given value is a solution of the inequality. q. h 7 < h; h =. q + 8 ; q = 6. Consider the inequalities < 0 and 6 <. a. Is = 0 a solution to both inequalities? b. Is = a solution to both inequalities? c. Find another value of that is a solution to both inequalities. Copyright Big Ideas Learning, LLC Big Ideas Math Red 0
2 8.. Practice B Write an inequality for the graph. Then, in words, describe all the values of that make the inequality true Write the word sentence as an inequality.. A number is at least.. A number r added to.7 is less than... A number h divided by is more than. 6. A number a minus 8. is no greater than. Tell whether the given value is a solution of the inequality. 7. p +.7 ; p = 9 8. y < ; y = 9..g 6; g = 0 0. d > ; d = Graph the inequality on a number line.... m >. To get a job at the local restaurant, you must be at least 6 years old. Write an inequality that represents this situation. Tell whether the given value is a solution of the inequality. q. t < t; t =. 0; < q q = 6. In order to qualify for a college scholarship, you must have acceptable scores in either the SAT or the ACT along with the following requirements: a minimum GPA of.; at least credits of college preparatory academic courses; and at least 7 hours of community service. a. Write and graph three inequalities that represent the requirements. b. Your cousin has a GPA of.6, credits of college preparatory class, and 6 hours of community service. Other than the test scores, does your cousin satisfy the requirements? Eplain. 0
3 . Puzzle Time What Do You Call A Bull That s Sleeping? Write the letter of each answer in the bo containing the eercise number. Write the word sentence as an inequality.. A number is greater than.8.. Twice a number is at most.. A number minus 9. is more than.6. Answers U..7 + < L. >.8 A... A number added to.7 is less than. 0 6 Tell whether the given value is a solution of the inequality...6.8; = 6.7 D. yes E. 6. > 0; = 6 6 Match each inequality with its graph >. 9. < R. L. 9. >.6 Z. B. no O
4 Name Date. Practice A. p <. s +. k 0. < n +. z 6. > + 6 t 7. d q >. 9. To stay within your budget, the area of the house and the garage combined is at most 000 square feet. The area of the garage is 8 square feet. Write and solve an inequality that represents the area of the house. 0. You have $7.6 in a bank account. The bank requires you to have at least $0 in your account or else you are charged a fee. Write and solve an inequality that represents the amount you can write your net check for without being charged a fee. Write and solve an inequality that represents.. The perimeter is less than 0 meters.. The perimeter is at least 8 feet. 8 m m ft ft ft ft. You need at least 000 points to earn a gift card from your bank. You currently have 700 points. a. Write and solve an inequality that represents the number of points you need to earn a gift card. b. You deposit money in your savings account and earn an additional 00 points. How does this change the inequality? Copyright Big Ideas Learning, LLC Big Ideas Math Red 09
5 . Practice B. y 7. w.8 <.. v + > 8. < + k. q r < > c p 0. >. 9. You and two friends are diving for lobster. The maimum number of lobsters you may have on your boat is 8. You currently have 7 lobsters. a. Write and solve an inequality that represents the additional lobsters that you may catch. b. Another friend comes on your boat and he has lobsters. You may now have lobsters on your boat. Write and solve an inequality that represents the additional lobsters that you may catch. c. How many lobsters is each person allowed to catch? Write and solve an inequality that represents. 0. The length is greater than the width.. The perimeter is less than or equal to 0 inches. 8 m 8 in. 8 in. + in. in. in.. The solution of w c >. is w >.. What is the value of c?. Describe all numbers that are solutions to <.. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. A triangle has side lengths of 6 inches and 7 inches. What are the possible values for the length of the third side? Eplain how you found your answer. 0
6 . Puzzle Time Did You Hear About The... A B C D E F G H I J K L M N Complete each eercise. Find the answer in the answer column. Write the word under the answer in the bo containing the eercise letter. GAME IN 6 AND 6 TIE THE < CATCHER < COLLARS Solve the inequality. A. + 0 B. > 6 C D. + E. 7 8 F. < G. 0 6 H. I. + + J.. < 7. K. > + 9 L. M < 0.8 O. To play on the football team, a seventh grader must weigh no more than 0 pounds. Your neighbor is in seventh grade and weighs 9 pounds. Write and solve an inequality that represents how much weight your neighbor can gain and still meet the requirement. THE > 0 BASEBALL < ENDED. WHICH > MITT 9 THE SOCKS >.8 THAT <. A SHIRTS BETWEEN
7 Name Date. Practice A. 8 > 8. r. >.6h. u 8... j < < Write the word sentence as an inequality. Then solve the inequality. 7. Five times a number is not less than. 8. The quotient of a number and is less than. 9. An SUV averages 6. miles per gallon. The maimum average number of miles that can be driven on a full tank of gas is 6 miles. Write and solve an inequality that represents the number of gallons in a tank. 0. p 0. v > g.. > y.. a. > 9h You are creating a decorative rope that is at least 0 feet long. a. To create the rope you are using beads that are 6 inches long. Write and solve an inequality that represents the number of beads that you can use. b. You do not have enough 6-inch beads to make the rope, so you will use 0-inch beads instead. Write and solve an inequality that represents the number of 0-inch beads that you can use. Copyright Big Ideas Learning, LLC Big Ideas Math Red
8 . Practice B. y.. < p 0..6g 0.8..k < 00 s < Write the word sentence as an inequality. Then solve the inequality. 7. A number divided by is at least. 8. The product of and a number is at most The solution of c is 8. What is the value of c? 0. 6t <. u q d > 8 j.. 0.8r The height of a room is 0 feet. You are building shelving from the floor to the ceiling. a. Each shelf requires 8 inches. Write and solve an inequality that represents the number of shelves that can be made. b. You forgot to include the thickness of each shelf in your measurements. The amount of space needed for each shelf is actually 0 inches. Write and solve an inequality that represents the number of shelves that can be made. Describe all numbers that satisfy both inequalities. Include a graph with your description. y 7. < and < 8. y and 6
9 . Puzzle Time What Do You Do When Your Smoke Alarm Goes Off? Write the letter of each answer in the bo containing the eercise number. Solve the inequality.. <. 6.. >... > > Three times a number is at least The quotient of 7 and a number is less than 8. Answers N. < 0 U. 6 R. < A. > 6. I. 6 T. < 6 F. E. > 6 T. R
10 Name Date. Practice A. m 7 <. r +. k + >...c 0. You are renting a moving truck for a day. There is a daily fee of $0 and a charge of $0.7 per mile. Your budget allows a maimum total cost of $6. Write and solve an inequality that represents the number of miles you can drive the truck. 6. ( b ) > 6 7. ( p ) d ( 6) 9.. < 0. ( a + ) 0. Write and solve an inequality that represents the values of for which the area of the rectangle will be at least square feet. ft. 7 + < 0. w 8w Your weekly base salary is $0. You earn $0 for each cell phone that you sell. a. What is the minimum amount you can earn in a week? b. Write and solve an inequality that represents the number of cell phones you must sell to make at least $60 a week. c. Write and solve an inequality that represents the number of cell phones you must sell to make at least $70 a week. d. The company policy is that as a part-time employee, the maimum you can earn each week is $90. Write and solve an inequality that represents the number of cell phones you can sell each week. Copyright Big Ideas Learning, LLC Big Ideas Math Red
11 8.. Practice B q. > v k n <.. An RV park receives $00 per month from each residential site that is occupied as well as $000 per month from their overnight sites. Write and solve an inequality to find the number of residential sites that must be occupied to make at least $,000 in revenue each month ( m ) > 0 7. ( f ) <.( p ) ( w.) 0. Write and solve an inequality that represents the values of for which the area of the rectangle will be at most square meters.. m v + 6v +. < An animal shelter has fied weekly epenses of $70. Each animal in the shelter costs an additional $6 a week. a. During the summer months, the weekly epenses are at least $70. Write and solve an inequality that represents the number of animals at the shelter for epenses to be at least $70 a week. b. During the winter months, the weekly epenses are at most $900. Write and solve an inequality that represents the number of animals at the shelter for epenses to be at most $900 a week. c. The cost for each animal has increased by $. What will be the maimum weekly epenses during the winter months?
12 . Puzzle Time What Did Ernie Say When Bert Asked Him If He Wanted Ice Cream? Write the letter of each answer in the bo containing the eercise number. Solve the inequality.. 8 < > > ( ) 0 Answers R. < T. 6 E. 7 S. 9. B. > U. < R. 8 E ( + ) ( + ) 8 6 7
13 Name Date Chapter Technology Connection For use after Section. Using Logical Tests in a Spreadsheet Epressions involving greater than, less than, and equal to are called logical tests because they can be either True or False. For eample, the logical test 0 > returns an answer of False. The logical test functions of a spreadsheet can be used to compare and categorize numbers. ACTIVITY Use logical tests to solve the following problem: A soccer team is in a tournament where each win earns points, a tie earns point, and a loss earns 0 points. Finish the spreadsheet to tally the points for the home team after five games. 6 7 A B C D E Home Team Away Team Win Loss Tie 7 0 Total Points SOLUTION Step Copy the chart above into a spreadsheet. Step In cell C, enter: =IF(A>B,, ""). The IF function performs the logical test that asks if the number in cell A is greater than the number in cell B. If it is true, then the cell will display a. If it is false, the double quotation marks will keep that cell blank. Net, copy and paste the formula from cell C to cells C, C, C, and C6. Your spreadsheet should change the formulas to correspond with the correct row. Step In cell D, enter: =IF(A<B, 0, ""). This formula puts a zero in the loss column if the score in cell A is less than the score in cell B. Copy and paste the formula down the column. Step In cell E, enter: =IF(A=B,, ""). This formula will find and award a single point for a tie. Copy and paste the formula down the column. Step Lastly, to find the sum of all your points, in cell D7 enter: =SUM(C:E6). So, the home team earned points. Copyright Big Ideas Learning, LLC Big Ideas Math Red
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