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

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Presentation transcript:

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

Aim: Compound Inequalities Course: Adv. Alg. & Trig x < 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 < Compound Inequality

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 x > x < {x | (x 2}

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

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

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

Aim: Compound Inequalities Course: Adv. Alg. & Trig. Model Problems Describe each compound inequality {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}

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

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

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

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