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

Slide 1Do Now:
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
Compound Inequality
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
-1
Aim: Compound Inequalities
9 < 3x + 6 and 3x + 6 < 15

{x |x > 4 x < –1}
Solve each separately
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 < –3 x > 0}
{x | x < –3 x > 5}
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
Model Problem
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?
x = # cm to remove
13.45 < 13.67 – x < 13.51