2. Aim: Compound Inequalities Course: Adv. Alg. & Trig. Aim: How do we solve compound inequalities? Do Now:

3. Aim: Compound Inequalities Course: Adv. Alg. & Trig. 0 1 234567 -7-6-5-4-3-2 x < 5 0 1 234567 -7-6-5-4-3-2 x > 1 Conjunctions Conjunction -Two simple sentences combined by using the word “and” Symbolically -  Graph the solution set of (x > 1)  (x < 5) x is a number greater than 1 and x is a number less than 5 1 < x < 5 0 1 234567 -7-6-5-4-3-2 Compound Inequality

4. Aim: Compound Inequalities Course: Adv. Alg. & Trig. Disjunctions Disjunction - Two simple sentences combined by using the word “or” Symbolically -  Graph the solution set of (x > 2)  (x < -1) x is a number greater than or equal to 2 or x is a number greater than -1 0 1 234567 -7-6-5-4-3-2 x > 2 0 1 234567 -7-6-5-4-3-2 x < -1 0 1 234567 -7-6-5-4-3-2 {x | (x 2}

5. Aim: Compound Inequalities Course: Adv. Alg. & Trig. 9 < 3x + 6 and 3x + 6 < 15  Solving Compound Inequalities Solve and graph 9 < 3x + 6 < 15 0 1 234567 -7-6-5-4-3-2 {x | 1 < x < 3} Method 1 –6 – 6 3 < 3x 1 < x –6 –6 3x < 9 x < 3 {x |(1 < x)  (x < 3)}

6. Aim: Compound Inequalities Course: Adv. Alg. & Trig. 9 < 3x + 6 < 15 Solving Compound Inequalities Solve and graph 9 < 3x + 6 < 15 0 1 234567 -7-6-5-4-3-2 {x | 1 < x < 3} Method 2 –6 – 6 – 6 3 < 3x < 9 1 < x < 3

7. Aim: Compound Inequalities Course: Adv. Alg. & Trig. x > 4  x < –1 Solving Compound Inequalities Solve and graph x – 3 > 1 or x + 2 < 1 0 1 234567 -7-6-5-4-3-2 {x |x > 4  x < –1} Solve each separately

8. Aim: Compound Inequalities Course: Adv. Alg. & Trig. Model Problems Describe each compound inequality. 0 1 234567 -7-6-5-4-3-2 0 1 234567 -7-6-5-4-3-2 0 1 234567 -7-6-5-4-3-2 {x | –3 < x < 3} x is greater than or equal to 0 or x is less than or equal to -3 x is greater than or equal to -3 and x is less than 3 x is greater than or equal to 5 or x is less than -3 {x | x 0} {x | x 5}

9. Aim: Compound Inequalities Course: Adv. Alg. & Trig. The ideal length of a both is 13.48 cm. The length can vary from the ideal by at most 0.03 cm. A machinist finds one both that is 13.67 cm long. By how much should the machinist decrease the length so the both can be used? Model Problem x = # cm to remove 13.48 – 0.03 < 13.67 – x < 13.48 + 0.03 13.45 < 13.67 – x < 13.51 -0.22 < – x < -0.16 0.22 < x < 0.16 ideal 13.48 cm maximum minimum tolerance

10. Aim: Compound Inequalities Course: Adv. Alg. & Trig. The Product Rule

11. Aim: Compound Inequalities Course: Adv. Alg. & Trig. The Product Rule

12. Aim: Compound Inequalities Course: Adv. Alg. & Trig. The Product Rule