Chapter 6 Review (Expressions, Equations, and Inequalities) 1. Cindy writes five different inequalities, as shown in the table below. Inequality 1 2𝑥 + 4 > 0 Inequality 2 3𝑥 − 2 ≥ −8 Inequality 3 −4𝑥 + 8 < 16 Inequality 4 −5𝑥 − 15 > −5 Inequality 5 −6𝑥 − 21 < −33 Cindy is asked by her teacher to graph the solution set to each of her inequalities. Cindy draws the graph below. -‐2 A. Inequality 1 B. Inequality 2 C. Inequality 3 D. Inequality 4 E. Inequality 5 2. Charlie has at most $50 to spend on pants. He wants to buy 3 identical pairs of pants and has a $10 off coupon. Write an inequality that models all possible prices, p, in dollars, for a pair of pants that Charlie can afford. 3. Sally is planning to take a trip. The cost of the plane ticket is $575. She earns $15 an hour (h) and has already saved $135. Write an inequality that shows the number of hours Sally could work in order to buy her ticket. 4. Matthew is buying supplies for his students. He is buying a notebook (n) and a pack of pencils for each of his 25 students. Each pack of pencils costs $1.25. If Matthew’s total cost is $156.25, write an equation that can be used to find how much each notebook will cost.
5. A teacher asks five different students to write an equation with a solution of x = 4. The students and their equations are shown below. Student Equation Aaron 2x + 6 = 2 Brad 2x – 9 = -‐1 Cathy -‐2x + 12 = 4 Doug 2(x + 2) = 10 Eric 2(x – 10) = -‐12 Which of the following students correctly wrote an equation with x = 4 as the solution? Select all that apply. A. Aaron B. Brad C. Cathy D. Doug E. Eric 6. Five students are each asked to solve an inequality and to graph the solution set on a number line. The students and their given inequalities are shown in the table below. Student Inequality Alex 2𝑥 − 1 ≤ −3 2 1 11 Carla − 𝑥 + ≤ 3 4 12 Mark 100𝑥 + 200 ≤ −300 York −1.5𝑥 − 2.3 ≥ −3.8 Vivian −5𝑥 + 1.2 ≥ 6.2 All five students graphed the solution set for their inequality as follows: -‐1 Which of the following students drew a correct graph of the solution set for their given inequality? A. Alex B. Carla C. Mark D. York E. Vivian
7. Which of the following word problems can be solved using the inequality 9x + 18 > 72? Select all that apply. A. Kim already has $18 and will make $9 per hour mowing lawns. How many hours, x, must Kim work to save at least $72? B. A plant is currently 18 mm tall. The plant grows at a rate of 9 mm every week. How many weeks, x, will it take the plant to become taller than 72 mm? C. Mary plans on running more than 72 miles. She has already run 18 miles and will run the same number of miles each day for the next 9 days. How many miles, x, must she run each day in order to meet her goal? 8. Four students are going on a trip. Each student needs at least $2000 for the trip. Each student writes an inequality that can be used to determine the number of weeks, x, that the student will need to save up the money needed for the trip. The inequalities are show in the table below. Student Inequality Liz 50𝑥 + 1400 ≥ 2000 Ricki 250𝑥 + 1000 ≥ 2000 Pedro 10𝑥 + 1200 ≥ 2000 Harold 150𝑥 + 200 ≥ 2000 Which of the following students wrote an inequality with a solution of 𝑥 ≥ 12? Select all that apply. A. Liz B. Ricki C. Pedro D. Harold
9. Which of the following word problems can be solved using the inequality 4𝑥 + 16 ≥ 48? Select all that apply. A. Darren has a collection of 16 postage stamps. He will collect 4 new stamps each month. How many months, x, will it take Darren for his stamp collection to have 48 or more postage stamps? B. Jamie wants to save at least $48 to buy a new video game. She has $16 and will save $4 every week. How many weeks, x, will it take Jamie to save up enough money to buy the video game? C. Karen is sending a package. She wants the package to have a minimum weight of 48 ounces. If the package already weighs 16 ounces, how many 4-‐ounce ornaments, x, can Karen place in the package? D. Irene is on a game show. She currently has 16 points. If she receives 4 points for correctly answering a question, how many additional questions, x, must she answer for her score to be greater than or equal to 48 points?
