1. 5-4 Compound Inequalities
Goal:
Solve and graph compound inequalities.
Eligible Content:
A / A / A

2. Vocabulary
Compound Inequality – 2 inequality statements connected by AND or OR.
OR statements – x is either greater than one number or less than another number.
AND statements – x is between two numbers.

3. x is a number greater than 1 or less than -2.
OR problems
x is a number greater than 1 or less than -2.
x > 1 OR x < -2

4. OR problems Always has the word OR in problem
2 separate inequalities pointing in opposite directions
Graph is always 2 shaded areas pointing away from each other. You shade OUTSIDE the points!

5. x is a number greater than 2 and less than 5.
AND problems
x is a number greater than 2 and less than 5.
x > 2 AND x < 5
2 < x < 5

6. AND problems Always has the word AND in written problem
1 inequality statement with 2 symbols pointing in the same direction (always< or ≤)
Graph always has shading BETWEEN 2 points

7. Examples Graph each compound inequality 3 < x ≤ 5
x > 5 OR x ≤ -2
-4 ≤ x ≤ -1
x ≥ 3 OR x < 1

8. Solving Compound Inequalities OR problems
2x + 3 < OR
2x < 2
x < 1
4x – 2 > x > x > 3
x < 1 OR x > 3

9. Examples 3x+ 1 < 4 OR 2x – 5 > 7 -6x – 5 > 7 OR 8x + 1 ≥ 25

10. Solve –2x + 5 > 15 or 5x + 15 > 20.
A. x > -5 or x > 1
B. x < –5 or x < 1
C. x < –5 or x > 1
D. x < 1

11. Solving Compound Inequalities AND problems
-2 ≤ 3x – 8 ≤ ≤ 3x ≤ ≤ x ≤ 6

12. Examples -5 ≤ 2x + 3 < 7 -2 < -2 – x < 1 -3 < -1 – 2x ≤ 5

13. Solve –3 < x – 2 < 5. Then graph the solution.
A. –1 < x < 7
B. –5 < x < 3
C. x < 7
D. –1 < x < 3

14. Weird AND problems
3x + 7 < 13 AND 5x + 2 > -13

15. REMEMBER WHEN YOU WRITE YOUR ANSWER:
OR problems – x should always be first
AND problems – x should be between 2 < symbols.

16. Practice
Worksheet – “5-4 Compound Inequalities”

17. Homework
Worksheet – “5-4 Compound Inequalities Homework”