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# EXAMPLE 5 - PowerPoint PPT Presentation

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

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Solve– 4 < 6x – 10 ≤ 14.

Then graph the solution.

ANSWER

The solutions are all real numbers greater than 1 and less than or equal to 4. The graph is shown below.

EXAMPLE 5

Solve an “and” compound inequality

– 4 < 6x – 10 ≤ 14

Write original inequality.

– 4 + 10< 6x – 10 + 10≤ 14 + 10

Add 10 to each expression.

6 < 6x ≤ 24

Simplify.

1 < x ≤ 4

Divide each expression by 6.

11 or 5x – 7 ≥ 23

Solve 3x + 5 ≤

EXAMPLE 6

Solve an “or” compound inequality

SOLUTION

A solution of this compound inequality is a solution of either of its parts.

First Inequality

Second Inequality

3x + 5 ≤ 11

5x – 7 ≥ 23

Write first inequality.

Write second inequality.

5x ≥ 30

3x ≤ 6

Add 7 to each side.

Subtract 5 from each side.

x ≥ 6

Divide each side by 5.

x ≤ 2

Divide each side by 3.

The graph is shown below. The solutions are all real numbers less than or equal to2or greater than or equal to6.

EXAMPLE 6

Solve an “or” compound inequality

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.

EXAMPLE 7

Write and use a compound inequality

5

9

5

9

5

Substitute for C.

(F – 32)

5

Multiply each expression by ,

the reciprocal of .

9

(F – 32)

9

EXAMPLE 7

Write and use a compound inequality

SOLUTION

The range of temperatures Ccan be represented by the inequality 18 ≤ C ≤ 34. Let Frepresent the temperature in degrees Fahrenheit.

18 ≤ C ≤ 34

Write inequality.

32.4 ≤ F – 32 ≤ 61.2

64.4 ≤ F ≤ 93.2

Add 32 to each expression.

The temperature of the monitor lizard ranges from 64.4°F to 93.2°F.

EXAMPLE 7

Write and use a compound inequality

–4 < x < 6

The solutions are all real numbers greater than – 4 and less than 6.

for Examples 5,6, and 7

GUIDED PRACTICE

Solve the inequality. Then graph the solution.

9. –1 < 2x + 7 < 19

x – 5

≤ 6

10. –8 ≤

ANSWER

–11≤ x ≤ 3

The solutions are all real numbers greater than and equal to – 11 and less than and equal to 3.

for Examples 5,6 and 7

GUIDED PRACTICE

Solve the inequality. Then graph the solution.

orx – 3 ≥ 7

11. x + 4 ≤ 9

x ≤ 5 orx ≥ 10

The graph is shown below. The solutions are all real numbers.

less than or equal to 5or greater than or equal to 10.

for Examples 5,6 and 7

GUIDED PRACTICE

Solve the inequality. Then graph the solution.

x < 0 orx ≥ 3

The graph is shown below. The solutions are all real numbers.

less than 0or greater than or equal to 3.

for Examples 5,6 and 7

GUIDED PRACTICE

Solve the inequality. Then graph the solution.

12. 3x – 1< –1 or 2x + 5 ≥ 11

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.

for Examples 5,6 and 7

GUIDED PRACTICE

ANSWER

15 ≤ C ≤ 30 or 59 ≤ F ≤ 86