1. Warm–up #4
Solve & Graph. Write solution in interval notation. 1. x – 5 < –10 or –4x + 4 ≥ x – 10 < –10 or –7x + 1 < – x + 4 < –4 and 8x + 10 ≥ –14

2. Warm-up #4 Solutions
1. x – 5 < –10 or –4x + 4 ≥ –4 –4 x < –5 or –4x ≥ 0 x < –5 or x ≤ 0
(–∞, 0] 00

3. Warm-up #4 Solutions
2. 3x – 10 < –10 or –7x + 1 < – –1 –1 x < 0 or –7x < –42 x < 0 or x > 6
(–∞, 0) ∪(6,∞) 00

4. Warm- up #4 Solutions
3. 8x + 4 < –4 and 8x + 10 ≥ –14 –4 –4 & –10 –10 8x < –8 & 8x ≥ – x < –1 and x ≥ –3
–3≤ x < –1
[–3, –1)

5. Homework Log Mon 10/12 Lesson 2 – 3 Learning Objective:
To solve absolute value inequalities
Hw: #208 Pg. 121 #41 – 49 odd Graph all, WS #1 – 4

6. 10/12/15 Lesson 2 – 3 Absolute Value Inequalities Day 2
Advanced Math/Trig

7. Learning Objective
To solve absolute value inequalities

8. Less Th”AND”
𝑥 <5
x < 5 AND x > –5
Great”OR”
𝑥 >5
x > 5 OR x < –5
Flip Inequality
& Change Sign!

9. Solve Absolute Value Inequalities
1. 2𝑥−1 <5 Less ThAND 2x – 1 < 5 and 2x – 1 > – x < 6 2x > – x < 3 and x > – 2 –2 < x < 3
(–2, 3)

10. Solve Absolute Value Inequalities
2. 3𝑥−4 ≤8 Less ThAND 3x – 4 ≤ 8 and 3x – 4 ≥ – x ≤ 12 3x ≥ – x ≤ 4 and x ≥ − 4 3 − 4 3 ≤ x ≤ 4
[− 4 3 , 3]

11. Solve Absolute Value Inequalities
3. 2𝑥+4 ≥6 GreatOR 2x + 4 ≥ 6 or 2x + 4 ≤–6 – 4 – 4 – 4 – 4 2x ≥ 2 2x ≤ – x ≥ 1 or x ≤ – 5
(–∞, –5] ∪ [1, ∞)

12. Solve Absolute Value Inequalities
4. 5𝑥+10 >25 GreatOR 5x + 10 > 25 or 5x + 10 < – 25 – 10 – 10 – 10 – 10 5x > 15 5x < – x > 3 or x < – 7
(–∞, –7] ∪ [3, ∞)

13. Solve Absolute Value Inequalities
5. −2𝑥+3 > – 4 All Real Numbers Absolute Value is always positive & will ALWAYS be greater than a negative number!!
(–∞, ∞)

14. Solve Absolute Value Inequalities
6. −3𝑥+4 <−12 No Solution Absolute Value is always positive & will NEVER be less than a negative number!! ∅

15. Solve Absolute Value Inequalities
−4𝑥 +2<−58 Get Absolute Value by itself!! 10 2−4𝑥 +2<−58 – 2 – −4𝑥 <− −4𝑥 <−6 No Solution!! ∅

16. Solve Absolute Value Inequalities
𝑥−1 −1>−37 Get Absolute Value by itself!! 4 8𝑥−1 −1>− 𝑥−1 >− 𝑥−1 > − 9 All Real Numbers!
(–∞, ∞)

17. Solve Absolute Value Inequalities
13. − 7 3𝑥+6 +9≤−117 − 7 3𝑥+6 ≤−126 3𝑥+6 ≥18 3x + 6 ≥ 18 or 3x + 6 ≤ − 18 3x ≥ 12 3x ≤ −24 x ≥ 4 or x ≤ −8
(–∞, –8] ∪ [4, ∞)

18. Solve Absolute Value Inequalities
14. −2 −4𝑥+2 −7>−43 −2 −4𝑥+2 >−36 −4𝑥+2 < < -4x + 2 < < - 4x < 16 5 > x > − 4 − 4 < x < 5
(–4, 5)

19. Ticket Out the Door Solve 2 3𝑥−5 −7<7 Graphing your solution
Write your answer in interval notation
Explain your process

20. #208 Pg. 121 #41 – 49 odd Graph all, WS #1 – 4
Homework
#208 Pg. 121 #41 – 49 odd Graph all, WS #1 – 4