Aim: Compound Inequalities Course: Adv. Alg. & Trig.

Aim: How do we solve compound inequalities?

Do Now:

Aim: Compound Inequalities Course: Adv. Alg. & Trig.

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1x < 5

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1x > 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 < 50 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1

Compound Inequality

Aim: Compound Inequalities Course: Adv. Alg. & Trig.

DisjunctionsDisjunction - 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 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1x > 2

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1x < -1

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1

{x | (x < -1) (x > 2}

Aim: Compound Inequalities Course: Adv. Alg. & Trig.

9 < 3x + 6 and 3x + 6 < 15

Solving Compound InequalitiesSolve and graph

9 < 3x + 6 < 15

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1

{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 InequalitiesSolve and graph

9 < 3x + 6 < 15

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1

{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 InequalitiesSolve and graph

x – 3 > 1 or x + 2 < 1

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1

{x |x > 4 x < –1}

Solve each separately

Aim: Compound Inequalities Course: Adv. Alg. & Trig.

Model ProblemsDescribe each compound inequality.

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1

0 1 2 3 4 5 6 7-7 -6 -5 -4 -3 -2 -1

{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 < –3 x > 0}

{x | x < –3 x > 5}

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

ideal13.48 cm

maximumminimum

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