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Math 78 Study Guide Unit 4: Linear Equations in One variable Name: _Key___________________ Knowledge and Understanding Math 1. What does absolute value represent? The distance a number is from zero; the amount of spaces the number is from zero on a number line; absolute value is always positive! 2. Explain the difference between an equation and an inequality. An equation is equal to something whereas an inequality is not equal; an equation has one exact solution whereas an inequality can have multiple/infinite solutions. 3. What are the possible solutions for an absolute value equation? Two solutions: usually positive and negative; one solution; or infinite solutions (│x│= x); no solution Proficiency of Skills 4. Solve for m. -6m + 8 = -16 -8 -8 -6m = -24 -6 -6 M = 4 5. Solve for z. 36x + 12y – 3z = 81 -36x-12y -36x-12y -3z = 81 – 36x – 12y -3 -3 -3 -3 Z = -27 + 12x + 4y 6. Solve for k. 6(k - 2) = 4k + 6 6k – 12 = 4k + 6 -4k -4k 2k – 12 = 6 +12 +12 2k = 18 2 2 K = 9 7. Solve for x: a. x6 8 b. x 6 8 c. x 6 0 X = 2; x = -14 no solution x = -6 8. Solve and graph the inequality. 6m – 32 ≤ 40 +32 +32 6m ≤ 72 6 6 M ≤ 12 • 4 5 6 7 8 9 10 11 12 Applications of Math 9. Write and solve the absolute value equation that represents the two numbers (x) that are 5 units away from 4 on a number line. │x - 4│= 5 x = -1; x = 9 10. Diane has a gift card for $75. She has spent $16 already. Write an inequality to determine the amounts that she can spend without exceeding the gift card amount. Then, solve and graph the amount. 75 ≥ 16 + x 59 ≥ x • 55 56 5758 5960 61 6263 Choose the best answer. 11. Write an inequality that best describes the following situation: Sara runs 30 minutes everyday. In the 30 minute workout, she burns 200 calories. If Sara wants to burn 700 calories a week, how many days will she need to run? X ≥ 700/200 12. Draw a graph that best displays the solution to this situation: Bob can spend $125 at Best Buy. In his cart, he has movies that each cost $17. What is the number of movies he can buy without exceeding his set amount? 125 ≥ 17x 7 ≥ x Graph should have a closed dot on 7 and should be shaded to the left. 13. Solve 7(8 +5 h) = - 84 56 + 35h = -84 -56 -56 35h = -140 35 35 H = -4 14. What is the solution of 5 x 7 14 8 ? -14 -14 5│x + 7│= -6 5 5 │x + 7│= -1.2 NO SOLUTION; THE ABSOLUTE VALUE CANNOT BE NEGATIVE 15. Solve. 2x+2 = 4x-6. -2x -2x 2 = 2x – 6 +6 +6 8 = 2x 2 2 X = 4 16. Solve xy-5 = k for y. +5 +5 Xy = k + 5 X x Y=k+5 x 17. Which statement can be modeled by x 3 12 ? a. Jennie sold 3 cookbooks. To earn a prize, Jennie must sell at least 12 cookbooks. b. Sam has 3 bottles of water. Together, Sam and Dave have at most 12 bottles of water. c. Peter has 3 baseball hats. Peter and his brothers have fewer than 12 baseball hats. d. Kathy swam 3 laps in the pool this week. She must swim more than 12 laps. 18. The ball used in a soccer game may not weigh more than 16 ounces or less than 14 ounces at 1 the start of the match. After 1 ounces of air was added to the ball, the ball was approved for 2 use in the game. Write a compound inequality to show how much the ball might have weighed before the air was added. Please look at the corrected answer!!! I had it backwards!!!! 12 ½ ≤ x ≤ 14 ½ 19. Businesses with profits less than $10,000 per year will be shut down. Write an inequality that represents this situation. X < 10,000