1. Compound Inequalities

2. What is a compound inequality
A compound in equality is two inequalities joined together by either the word “and” or “or” X < 2 or x > 7 Read as: “x is less than 2 or x is greater than 7” X > 3 and x < 8 Read as: “x is greater than 3 and x is less than 8” However we usually see “and” statements like this 5 < x < 10 Read as: “x is greater than 5 and less than 10”

3. Solving an OR problem Just solve the left side and then the right side
Graph both pieces on the number line
3x > or -4x > 20
Divide by 3 divide by -4
x > or x < -5
-5 4
The solutions are still where the arrows point.

4. Solving an AND problem
10 < 2x+4 < 28 You are trying to get x by itself
So subtract 4 from ALL sides
6 < 2x < 24 Now divide ALL sides by 2
3 < x < 12 The final answer is:
x is greater than 3 and less than 12

5. Graphing AND Statements
3 < x < 12
To graph:
put the two numbers on the number line.
Draw open or closed circles.
Connect the circles with a line segment (no arrows)

6. The hard part
And statements always have to be written in this format: smaller # < x< bigger # The inequality arrows always face this direction in the end. The smaller number is always on the left The bigger number is always on the right

7. The hard part (continued)
It becomes difficult when you divide by a negative. 8 < -2x ≤ 20 When you divide both sides by you have to flip the signs and get -4 > x ≥ -10 The problem is that this is no in the proper format so we have to switch everything back -10 ≤ x <-4 Note that the “same alligator” is eating the same number. I.e. Keep the equal sign with the same thing.

8. Practice Solve and Graph on a Number Line
2x + 5 > 13 or 3x + 5 < -13
14 ≤ 3x+5 ≤ 32

9. Answers to practice
x > 4 or x < -6
-6 4
3 ≤ x ≤ 9
3 9