1. Solve an “and” compound inequality
EXAMPLE 5
Solve an “and” compound inequality
Solve – 4 < 6x – 10 ≤ 14.
Then graph the solution.
– 4 < 6x – 10 ≤ 14
Write original inequality.
– < 6x – ≤
Add 10 to each expression.
6 < 6x ≤ 24
Simplify.
1 < x ≤ 4
Divide each expression by 6.
ANSWER
The solutions are all real numbers greater than 1 and less than or equal to 4. The graph is shown below.

2. Solve an “or” compound inequality
EXAMPLE 6
Solve an “or” compound inequality
Solve 3x + 5 ≤
11 or 5x – 7 ≥ 23
. Then graph the solution.
SOLUTION
A solution of this compound inequality is a solution of either of its parts.
First Inequality
Second Inequality
3x + 5 ≤ 11
Write first inequality.
5x – 7 ≥ 23
Write second inequality.
3x ≤ 6
5x ≥ 30
Subtract 5 from each side.
Add 7 to each side.
x ≥ 6
x ≤ 2
Divide each side by 3.
Divide each side by 5.

3. EXAMPLE 6
Solve an “or” compound inequality
ANSWER
The graph is shown below. The solutions are all real numbers less than or equal to 2 or greater than or equal to 6.

4. EXAMPLE 7
Write and use a compound inequality
Biology
A monitor lizard has a temperature that ranges from 18°C to 34°C. Write the range of temperatures as a compound inequality. Then write an inequality giving the temperature range in degrees Fahrenheit.

5. Write and use a compound inequality
EXAMPLE 7
Write and use a compound inequality
SOLUTION
The range of temperatures C can be represented by the inequality 18 ≤ C ≤ 34. Let F represent the temperature in degrees Fahrenheit.
18 ≤ C ≤ 34
Write inequality.
18 ≤ ≤ 34 5 9
( F – 32)
Substitute for C. 9 5
( F – 32)
Multiply each expression by ,
the reciprocal of 9 5
32.4 ≤ F – 32 ≤ 61.2
64.4 ≤ F ≤ 93.2
Add 32 to each expression.

6. EXAMPLE 7
Write and use a compound inequality
ANSWER
The temperature of the monitor lizard ranges from 64.4°F to 93.2°F.

7. Solve the inequality. Then graph the solution.
GUIDED PRACTICE
for Examples 5,6, and 7
Solve the inequality. Then graph the solution.
9. – 1 < 2x + 7 < 19
– 1 < 2x + 7 < 19
Write original inequality.
– 1– 7 < 2x + 7 – 7 < 19 – 7
Subtract 7 from each expression.
– 8 < 2x < 12
Simplify.
– 4 < x < 6
Divide each expression by 2.
ANSWER
The solutions are all real numbers greater than – 4 and less than 6.

8. Solve the inequality. Then graph the solution.
GUIDED PRACTICE
for Examples 5,6 and 7
Solve the inequality. Then graph the solution.
10. – 8 ≤
– x – 5
≤ 6
– 8 ≤
– x – 5
≤ 6
Write original inequality.
– 8+5 ≤
– x – 5 + 5
≤ 6 + 5
Add 5 to each expression.
– 3 ≤
– x
≤ 11
– 11 ≤ x
≤ 3
Simplify.
The solutions are all real numbers greater than and equal to – 11 and less than and equal to 3.
ANSWER

9. Solve the inequality. Then graph the solution.
GUIDED PRACTICE
for Examples 5,6 and 7
Solve the inequality. Then graph the solution.
11. x + 4 ≤
9 or x – 3 ≥ 7
SOLUTION
A solution of this compound inequality is a solution of either of its parts.
First Inequality
Second Inequality
x + 4 ≤ 9
Write first inequality.
x – 3 ≥ 7
Write second inequality.
x ≤ 5
Subtract 4 from each side.
x ≥ 10
Add 3 to each side.

10. GUIDED PRACTICE
for Examples 5,6 and 7
ANSWER
The graph is shown below. The solutions are all real numbers.
less than or equal to 5 or greater than or equal to 10.

11. Solve the inequality. Then graph the solution.
GUIDED PRACTICE
for Examples 5,6 and 7
Solve the inequality. Then graph the solution.
12. 3x – 1 < – 1 or 2x + 5 ≥ 11
SOLUTION
A solution of this compound inequality is a solution of either of its parts.
First Inequality
Second Inequality
3x – 1< – 1
Write first inequality.
2x + 5 ≥ 11
Write second inequality.
3x ≤ 0
2x ≥ 6
Add 1 each side .
Subtract 5 from each side
x ≥ 3
x ≤ 0
Divide each side by 3.
Divide each side by 5.

12. GUIDED PRACTICE
for Examples 5,6 and 7
less than 0 or greater than or equal to 3.
ANSWER
The graph is shown below. The solutions are all real numbers.

13. GUIDED PRACTICE for Examples 5,6 and 7 13.
WHAT IF? In Example 7, write a compound inequality for a lizard whose temperature ranges from 15°C to 30°C. Then write an inequality giving the temperature range in degrees Fahrenheit.
SOLUTION
The range of temperatures C can be represented by the inequality 15 ≤ C ≤ 30. Let F represent the temperature in degrees Fahrenheit.
15 ≤ C ≤ 30
Write inequality.
15 ≤ ≤ 30 5 9
( F – 32)
Substitute for C. 9 5
( F – 32)

14. The temperature of the monitor lizard ranges from 59°F to 86°F.
GUIDED PRACTICE
for Examples 5,6 and 7
Multiply each expression by ,
the reciprocal of 9 5
27 ≤ F – 32 ≤ 54
59 ≤ F ≤ 86
Add 32 to each expression.
ANSWER
The temperature of the monitor lizard ranges from 59°F to 86°F.