3. $100 $200 $300 $400 $500 $200 $300 $400 $500 Graphing Inequalities One Step Inequalities Absolute Value Multi-Step Inequalities Compound Inequalities

4. Graphing Inequalities for $100 Graph the inequality shown below: x > -4

5. Answer Back X > -4

6. Graphing Inequalities for $200 Write an inequality for the graph shown below:

7. Answer Back X ≤ 3

8. Graphing Inequalities for $300 Graph the inequality shown below: -7 < x

9. Answer Back -7 < x

10. Graphing Inequalities for $400 Graph the inequality shown below: 0 ≤ x < 4

11. Answer Back 0 ≤ x < 4

12. Graphing Inequalities for $500 Graph the inequality shown below. Check your answer: x < -5 or x ≥ 2

13. Answer Back x < -5 or x ≥ 2 Let x = -7 Let x = -4 Let x = 5 -7 True -4 NOT True 5 NOT True -7 ≥ 2 =>NOT True -4 ≥ 2 => NOT True 5 ≥ 2 => True

14. One-Step Inequalities for $100 Solve for x: X + 2 < 1

15. Answer X + 2 < 1 -2 -2 X < -1 Back

16. One-Step Inequalities for $200 Solve for x: x/(-5) > 7

17. Answer x/(-5) > 7 x/(-5) * (-5) > 7 * (-5) X < -35 Back

18. One-Step Inequalities for $300 Solve for x: 4x ≥ -36

19. Answer 4x ≥ -36 (4x)/(4) ≥ (-36)/(4) x ≥ -9 Back

20. One-Step Inequalities for $400 Write the following inequality in words: x + 5 ≥ 7

21. Answer Back x + 5 ≥ 7 Five more than a number, x, is greater than or equal to 7

22. One-Step Inequalities for $500 Write an Inequality to model the following situation: Mr. Sam spent at least 4 hours making this game

23. Answer Back Let t = the time Mr. Sam spent making this game Then, t ≥ 4 hours

24. Multi-Step Inequalities for $100 Solve for x: x/(3) + 3 > 5

25. Answer x/(3) + 3 > 5 x/(3) + 3 - 3 > 5 - 3 x/(3) > 2 x/(3) * 3 > 2 * 3 X > 6 Back

26. Multi-Step Inequalities for $200 Solve for x: -5x + 20 ≤ 10

27. Answer -5x + 20 ≤ 10 -20 -20 -5x ≤ -10 (-5x)/(-5)≤ (-10)/(-5) X ≥ 2 Back

28. Multi-Step Inequalities for $300 Replace the with a number that makes the inequalities equivalent -3x > x < -9

29. Answer -3x > (-3x)/(-3) > / (-3) x < /(-3) and x < -9 So, /(-3) = -9 /(-3) * -3 = -9 * -3 = 27 Back

30. Multi-Step Inequalities for $400 Solve for x: -(x-6) + 5 - 2x < 8

31. Answer -(x-6) + 5 - 2x < 8 -(x-6) + 5 - 5 - 2x < 8 – 5 -(x-6) - 2x < 3 -x + 6 – 2x < 3 -3x + 6 < 3 -3x + 6 – 6 < 3 – 6 -3x < -3 (-3x)/(-3) < (-3)/(-3) X > 1 Back

32. Multi-Step Inequalities for $500 Solve for x. CHECK YOUR ANSWER 10x – 5 - 3x > 3 – (5 - x)

33. Answer 10x – 5 - 3x > 3 – (5 - x) 7x – 5 > 3 – 5 + x 7x – 5 > -2 + x 7x > 3 + x 6x > 3 x > 0.5 Back Check 1: (Substitute it in –> Should be equal) 10(0.5) – 5 – 3(0.5) = 3 – (5 – (0.5)) 5 - 5 – 1.5 = 3 - 4.5 -1.5 = -1.5 Check 2: (Pick value that is true) Let x = 1 10(1) – 5 – 3(1) > 3 – (5 – (1)) 10 - 5 – 3 > 3 - 4 2 > -1 => True Check 3: (Pick value that is false) Let x = 0 10(0) – 5 – 3(0) = 3 – (5 – (0)) -5 > 3 - 5 -5 > -2 => FALSE

34. Compound Inequalities for $100 Write a compound inequality that models the graph:

35. Answer X < -3 or X ≥ -1 Back

36. Compound Inequalities for $200 Solve the following inequality: |-2(3-x) +2| -1 > 11

37. Answer |-2(3-x) +2| -1 > 11 |-2(3-x) +2| -1 + 1 > 11 + 1 |-2(3-x) +2| > 12 |-6+2x +2| > 12 |2x -4| > 12 2x -4 > 12 or 2x -4 < -12 2x > 16 or 2x < -8 x > 8 or x < -4 Back

38. Compound Inequalities for $300 Solve the following inequality: 1 ≤ -2x -1 < 7

39. Answer 1 ≤ -2x -1 < 7 1+1 ≤ -2x – 1 + 1 < 7+1 2 ≤ -2x < 8 2/(-2) ≤ (-2x)/(-2) < 8/(-2) -1 ≥ x > -4 Back

40. Compound Inequalities for $400 Solve the following inequality: -5< 7x + 2 ≤ 9

41. Answer -5< 7x + 2 ≤ 9 -5 – 2 < 7x + 2 – 2 ≤ 9 – 2 -7 < 7x ≤ 7 (-7)/7 < (7x)/7 ≤ 7/7 -1 < x ≤ 1 Back

42. Compound Inequalities for $500 Write an Inequality to model the following situation: Mr. Steven is trying to decide whether he wants to buy an automatic or a manual motorbike. If he buys an automatic motorbike, then he will spend at least $850. If he buys a manual bike, then he will spend less than $600.

43. Answer Let C = the cost of the motorbike Then, C ≥ $850 or C < $600 Back

44. Absolute Value for $100 Define: absolute value

45. Answer Absolute Value – The distance a number is away from zero (the origin) Back

46. Absolute Value for $200 Solve the following inequality: |3x + 1.5| ≥ 10.5

47. Answer |3x + 1.5| ≥ 10.5 3x + 1.5 ≥10.5 or 3x + 1.5 ≤ -10.5 3x ≥ 9 or 3x ≤ -12 x ≥ 3 or x ≤ -4 Back

48. Absolute Value for $300 Solve the following inequality: 2-3|x+1| = -13

49. Answer 2-3|x+1| = -13 -3|x+1| = -15 |x+1| = 5 x+1 = 5 or x+1 = -5 x = 4 or x = -6 Back

50. Absolute Value for $400 Solve the following inequality: -5*|x – 3| + 5 > 30

51. Answer -5*|x – 3| + 5 > 30 -5*|x – 3| + 5 – 5 > 30 - 5 -5*|x – 3| > 25 (-5*|x – 3|)/(-5) > 25/(-5) |x – 3| < -5 NO SOLUTION => Absolute Value can never be negative Back

52. Absolute Value for $500 Solve and graph the following inequality: 8 + 2*|3-(2+x)| < 24

53. Answer Back 8 + 2*|3-(2+x)| < 24 8 - 8 + 2*|3-(2+x)| < 24 - 8 2*|3-(2+x)| < 16 |3-(2+x)| < 8 |3-2-x| < 8 |1 – x| < 8 1 - x -8 -x -9 x > -7 and x < 9