1. Solving Compound Inequalities
6.3
Goal
Solve and graph compound inequalities
Key Words
compound inequality
conjunction
disjunction

2. Definition
A compound inequality consists of two inequalities connected by the word and or the word or.
Examples
-7 < x < x < 8 or x > 27
x < - 4 or x >  x  30

3. EXAMPLE 1
Write Compound Inequalities with AND
Write a compound inequality that represents the set of all real numbers greater than or equal to 0 and less than 4. Then graph the inequality.

4. Checkpoint Graph an Inequality in One Variable.
Write a verbal sentence that describes the inequality. Then graph the inequality.
-2 < y < 0
7  t  8
4  n < 11

5. MOUNTAIN PLANT LIFE Compound Inequalities in Real Life
EXAMPLE 2
Compound Inequalities in Real Life
MOUNTAIN PLANT LIFE
Write a compound inequality that describes the approximate elevation range for the type of plant life on Mount Rainier, a mountain peak in Washington.
Trees below 6000 feet
Alpine flowers below 7500 feet
No trees or alpine flowers at or below 14,410 feet

6. Solve -2 < x + 2  4. Then graph the solution.
EXAMPLE 3
Solve Compound Inequalities with AND
Solve -2 < x + 2  4. Then graph the solution.
Method 1

7. Solve -2 < x + 2  4. Then graph the solution.
EXAMPLE 3
Solve Compound Inequalities with AND
Solve -2 < x + 2  4. Then graph the solution.
Method 2

8. Checkpoint Use Subtraction to Solve an Inequality
Choose a method from Example 3 to solve the inequality. Then graph the solution.
-1 < x + 3 < 7
-6  3x  12

9. Solve – 2 < – 2 – x < 1. Then graph the solution.
EXAMPLE 5
Reverse Both Inequalities
Solve – 2 < – 2 – x < 1. Then graph the solution.

10. Checkpoint Use Subtraction to Solve an Inequality
Solve the inequality. Then graph the solution.
3  2x + 3  7
– 6  – 3x  12

11. EXAMPLE 1
Write Compound Inequalities with OR
Write a compound inequality that represents the set of all real numbers less than or equal to -1 or greater than 3. Then graph the inequality.

12. Checkpoint Graph an Inequality in One Variable.
Write a verbal sentence that describes the inequality. Then graph the inequality.
1. y < 0 or y > 5
y < -3 or y > 5
y < 7 or y > 11

13. Solve 3x + 1  4 or 2x – 5  7. Then graph the solution.
EXAMPLE 3
Solve Compound Inequalities with OR
Solve 3x + 1  4 or 2x – 5  7. Then graph the solution.

14. Solve: x - 4  -8 or x + 3  5. Then graph the solution.
EXAMPLE 3
Solve Compound Inequalities with OR
Solve: x - 4  -8 or x + 3  5. Then graph the solution.

15. Checkpoint Use Subtraction to Solve an Inequality
Solve the inequality. Then graph the solution.
7x  42 or x + 5  7
x + 7  3 or 5x + 5  10

16. Solve 2 – 10 x  -28 or -9x – 6  21. Then graph the solution.
EXAMPLE 5
Reverse Both Inequalities
Solve 2 – 10 x  -28 or -9x – 6  21. Then graph the solution.

17. Homework
p. 349 #12-38 evens, 39, 40, 45, 50, 62, 65