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EXAMPLE 5

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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EXAMPLE 5

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  1. 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.

  2. . Then graph the solution. 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.

  3. ANSWER 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

  4. 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. EXAMPLE 7 Write and use a compound inequality

  5. 18 ≤ ≤ 34 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.

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

  7. ANSWER –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

  8. –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.

  9. ANSWER 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.

  10. ANSWER 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

  11. 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. for Examples 5,6 and 7 GUIDED PRACTICE ANSWER 15 ≤ C ≤ 30 or 59 ≤ F ≤ 86

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