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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