Unit 4 Inequalities

1. Unit 4 Inequalities • Graphing Inequalities • Translating Inequality Words • Solving Inequalities • Inequality Word Problems

2. Inequalities OBJECTIVE: Given five inequalities, the student will be able to solve for the variable and graph the result with 80% accuracy. Ca.SS 5.0: Students solve multi-step equations involving linear inequalities.

3. 1. 5y + 8 < -92 2. -7 – 10y 5 – 7y 3. 4. 0.6x – 1.8  1.2 x Check for Understanding

4. = Inequalities

5. = NOT Inequalities

6. Larger # Smaller # Smaller # Larger # Inequalities Greater Than Less Than

7. ≥ Greater than or equal > Greater than ≤ Less than or equal <Less than  ≥ -7 -6 -5 -4 -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10  >  ≤  < Graphing Inequalities X ≥ 1 X > 5 X ≤ -3 X < 0

8. X ≥ 8 -7 -3 -3 The Only Way They Are Different From Regular Equations is… If there is a negative coefficient, then you ; • Treat the inequality exactly the same as you would solve an equation • Then change the direction of the “inequality” on the last step. -3X < -18 (-7) (-7) X > 6 X ≤ -56

9. 8y –4 < -52 +4 +4 8y < -48 8 8 y < -6 15x + 3–14x 7 x + 3  7 -3 -3 x  4 Try These… 8y –4 < -52 15x + 3 –14x 7

10. 6 – 8m> 22 -6 -6 - 8m > 16 -8 -8 m < -2 7 – 8y 5 – 7y +7y +7y 7 – x  5 -7 -7 - x  -2 -1 -1 x 2 Try These… 6 – 8m> 22 7 – 8y 5 – 7y

11. 10 – 3x  4 -10 -10 -3x  -6 -3 -3 x  2 Try These… 5 3 1 •15 • 15 • 15

12. 0.3x + 5.4  -1.0x + 0.2 Move every decimal over 1 place 3x + 54  -10x + 2 +10x +10x 13x + 54  2 -54 -54 13x  -52 13 13 x  -4 Try These… 0.3x+5.4  -x+0.2

13. 1. 5y + 8 < -92 2. -7 – 10y 5 – 7y 3. 4. 1.2 x  0.6x – 1.8 Check for Understanding y< -20 y -3 x 1 x -3

14. Summary Inspiration: • What do the following inequalities mean? >  ≤  • What do you do when you multiply or divide by a negative? • How is solving inequalities like solving equations?

15. Writing Inequalities OBJECTIVE: Given 5 word problems, the student will be able to write the inequality with 80% accuracy. Ca.SS 5.0: Students solve multi-step equations involving linear inequalities.

16. Check for Understanding • A number is less than 7 • 5 more than a number is at least 3 • 13 less than x is more than 5 • Twice a number m is at most –4 • The number x is at least as great as the number y

17. You always need to think about $$$ in your pocket The approach… If I have at least 5 dollars in my pocket…

18. You always need to think about $$$ in your pocket The approach… Then I have 5 dollars or more (greater than or =)

19. You always need to think about $$$ in your pocket The approach… If I have at most 30 dollars in my pocket Then I have 5 dollars or more (greater than or =)

20. You always need to think about $$$ in your pocket The approach… Then I have 30 dollars or less (less than or =) Then I have 5 dollars or more (greater than or =)

21. You always need to think about $$$ in your pocket The approach… Then I have 30 dollars or less (less than or =) Then I have 5 dollars or more (greater than or =) If I have more than 50 dollars…

22. You always need to think about $$$ in your pocket The approach… Then I have 30 dollars or less (less than or =) Then I have 5 dollars or more (greater than or =) Then I have $50.01 or more (greater than) If I have less than 17 dollars… By Marianne Ilmanen

23. You always need to think about $$$ in your pocket The approach… Then I have 30 dollars or less (less than or =) Then I have 5 dollars or more (greater than or =) Then I have $50.01 or more (greater than) Then I have $16.99 or less (less than) By Marianne Ilmanen

24. Inequalities in Word Problems A number decreased by negative 4 is at least 9. A numberdecreased by negative 4is at least 9. X – (-4) ≥ 9 X +4≥ 9

25. At the maximum $9 At most $9 Greater than $9 At the minimum $9 Less than $9 At least $9 No more than $9 No less than $9 X  9 The Amount of Money in your Pocket is…. • X  9 • X  9 X  9 Interpretation Trick • X  9 • X  9 • X  9 X  9

26. Let’s Try a Few A number “Y” is less than 4

27. Let’s Try a Few Y < 4 A number “Y” is less than 4

28. Let’s Try a Few Y < 4 A number “Y” is less than 4 A number “X” is greater than or equal to 2 ½

29. Let’s Try a Few Y < 4 A number “Y” is less than 4 A number “X” is greater than or equal to 2 ½ X  2 ½

30. Let’s Try a Few Y < 4 A number “Y” is less than 4 A number “X” is greater than or equal to 2 ½ X  2 ½ A number “M” is at least 3

31. Let’s Try a Few Y < 4 A number “Y” is less than 4 A number “X” is greater than or equal to 2 ½ X  2 ½ A number “M” is at least 3 M  3 "At least" means equal or more...

32. Let’s Try a Few A number “P” is at most –4

33. Let’s Try a Few P  -4 A number “P” is at most –4

34. Let’s Try a Few P  -4 A number “P” is at most –4 3 less than a number is at least 10

35. Let’s Try a Few P  -4 A number “P” is at most –4 3 less thana numberis at least 10 X – 3 10

36. Let’s Try a Few P  -4 A number “P” is at most –4 3 less thana numberis at least 10 X – 3 10 6 times a number is greater than - 1

37. Let’s Try a Few P  -4 A number “P” is at most –4 3 less thana numberis at least 10 X – 3 10 6 timesa numberis greater than - 1 6m  -1

38. Let’s Try a Few 13 less than twice a number is at least –6

39. Let’s Try a Few 2x – 13 -6 13 less than twice a number is at least –6

40. Let’s Try a Few 2x – 13 -6 13 less than twice a number is at least –6 7 more than half of a number is at most 5

41. Let’s Try a Few 2x – 13 -6 13 less than twice a number is at least –6 ½ x + 7 5 7 more than half ofa numberis at most 5

42. Let’s Try a Few 7 more than a number is more than –17

43. Let’s Try a Few X + 7 -17 7 morethana numberis more than –17

44. Let’s Try a Few X + 7 -17 7 morethana numberis more than –17 -15 less than “P” cubed is at least 35

45. Let’s Try a Few X + 7 -17 7 morethana numberis more than –17 -15 less than“P” cubedis at least 35 P3+ 15  35

46. Check for Understanding X< 7 X + 5  3 • A number is less than 7 • 5 more than a number is at least 3 • 13 less than x is more than 5 • Twice a number m is at most –4 • The number x is at least as great as the number y X – 13  5 2m -4 X Y

47. Summary Inspiration • Describe the “trick” to interpreting the correct inequality from word problems. • What do inequalities mean? • How do Inequalities apply to your reality?