Warm–up #4 Solve & Graph. Write solution in interval notation. 1. x – 5 < –10 or –4x + 4 ≥ 4 2. 3x – 10 < –10 or –7x + 1 < –41 3. 8x + 4 < –4 and 8x +

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Warm–up #4 Solve & Graph. Write solution in interval notation. 1. x – 5 < –10 or –4x + 4 ≥ 4 2. 3x – 10 < –10 or –7x + 1 < –41 3. 8x + 4 < –4 and 8x + 10 ≥ –14

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

Warm-up #4 Solutions 2. 3x – 10 < –10 or –7x + 1 < –41 +10 +10 –1 –1 x < 0 or –7x < –42 x < 0 or x > 6 (–∞, 0) ∪(6,∞) 00

Warm- up #4 Solutions 3. 8x + 4 < –4 and 8x + 10 ≥ –14 –4 –4 & –10 –10 8x < –8 & 8x ≥ –24 8 8 8 8 x < –1 and x ≥ –3 –3≤ x < –1 [–3, –1)

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

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

Learning Objective To solve absolute value inequalities

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

Solve Absolute Value Inequalities 1. 2𝑥−1 <5 Less ThAND 2x – 1 < 5 and 2x – 1 > – 5 + 1 +1 +1 +1 2x < 6 2x > – 4 2 2 2 2 x < 3 and x > – 2 –2 < x < 3 (–2, 3)

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

Solve Absolute Value Inequalities 3. 2𝑥+4 ≥6 GreatOR 2x + 4 ≥ 6 or 2x + 4 ≤–6 – 4 – 4 – 4 – 4 2x ≥ 2 2x ≤ – 10 2 2 2 2 x ≥ 1 or x ≤ – 5 (–∞, –5] ∪ [1, ∞)

Solve Absolute Value Inequalities 4. 5𝑥+10 >25 GreatOR 5x + 10 > 25 or 5x + 10 < – 25 – 10 – 10 – 10 – 10 5x > 15 5x < – 35 5 5 5 5 x > 3 or x < – 7 (–∞, –7] ∪ [3, ∞)

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

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

Solve Absolute Value Inequalities 11. 10 2−4𝑥 +2<−58 Get Absolute Value by itself!! 10 2−4𝑥 +2<−58 – 2 – 2 10 2−4𝑥 <−60 10 10 2−4𝑥 <−6 No Solution!! ∅

Solve Absolute Value Inequalities 12. 4 8𝑥−1 −1>−37 Get Absolute Value by itself!! 4 8𝑥−1 −1>−37 + 1 + 1 4 8𝑥−1 >−36 4 4 8𝑥−1 > − 9 All Real Numbers! (–∞, ∞)

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, ∞)

Solve Absolute Value Inequalities 14. −2 −4𝑥+2 −7>−43 −2 −4𝑥+2 >−36 −4𝑥+2 <18 -18 < -4x + 2 < 18 - 20 < - 4x < 16 5 > x > − 4 − 4 < x < 5 (–4, 5)

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

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