1. 6.3 Compound Inequalities
Objective:
How to solve and graph compound inequalities
How to model a real life situation with a compound inequality

2. Learn to Read… a< x <b Read: x is between a and b a< x < b
Read: x is between a & b inclusive

3. Graph: 1< x < 5
Read as: ?
x is between 1 and 5 1 2 3 4 5 6 7

4. x greater than 2 or x less than -1
Write the inequality
x greater than 2 or x less than -1
x < -1 x > 2
Graph: -2 -1 1 2 3
*Remember:
(closed circle) • when the number is included!

5. Solve Compound Inequalities and Graph:
Solve like an equation, but now you have three parts!
-9 < 6x + 3 ≤ 39
Subtract 3 from all three parts. -3 -3 -3
-12 < 6x ≤ 36
Divide each part by 6. 6 6 6
-2 < x ≤ 6
GRAPH: -3 -2 -1 1 2 3 4 5

6. Write the inequality, solve and then graph:
Eight plus two times a number is less than six.
8 + 2x < 6
2x < -2
x < -1 -2 -1 1 2 3

7. Write the inequality, solve and then graph:
Eight times a number x plus 4 is between -4 and 20.
-4< 8x + 4 < 20
-8 < 8x < 16
-1 < x < 2 -2 -1 1 2 3
The numbers should be displayed least to greatest
Example you would not write 2 > x > -1

8. Practice: Graph 1. x > 4 or x < -2 2. -2 < x < 3 Solve -1 1 2 -2 -1 1 2 3
Solve
x > 3
3 < 2 - x < 5
Same thing as..
But # line order
5. Write an inequality for the following graph
4≤ x ≤ 8