 # EXAMPLE 5 Solve an and compound inequality Solve

• Slides: 11 EXAMPLE 5 Solve an “and” compound inequality Solve – 4 < 6 x – 10 ≤ 14. Then graph the solution. – 4 < 6 x – 10 ≤ 14 Write original inequality. – 4 + 10 < 6 x – 10 + 10 ≤ 14 + 10 Add 10 to each expression. 6 < 6 x ≤ 24 1<x≤ 4 Simplify. 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. EXAMPLE 6 Solve an “or” compound inequality Solve 3 x + 5 ≤ 11 or 5 x – 7 ≥ 23. Then graph the solution. SOLUTION A solution of this compound inequality is a solution of either of its parts. First Inequality 3 x + 5 ≤ 11 Write first inequality. 3 x ≤ 6 Subtract 5 from each side. x ≤ 2 Divide each side by 3. Second Inequality 5 x – 7 ≥ 23 Write second inequality. 5 x ≥ 30 Add 7 to each side. x ≥ 6 Divide each side by 5. 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. 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. 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. Write inequality. 18 ≤ C ≤ 34 5 5 (F – 32) Substitute (F – 32) for C. 18 ≤ ≤ 34 9 9 Multiply each expression by 9 , 32. 4 ≤ F – 32 ≤ 61. 2 5 5. 9 Add 32 to each expression. the reciprocal of 64. 4 ≤ F ≤ 93. 2 EXAMPLE 7 Write and use a compound inequality ANSWER The temperature of the monitor lizard ranges from 64. 4°F to 93. 2°F. GUIDED PRACTICE for Examples 5, 6, and 7 Solve the inequality. Then graph the solution. 9. – 1 < 2 x + 7 < 19 ANSWER – 4 < x < 6 The solutions are all real numbers greater than – 4 and less than 6. GUIDED PRACTICE for Examples 5, 6 and 7 Solve the inequality. Then graph the solution. 10. – 8 ≤ –x – 5 ≤ 6 ANSWER – 11 ≤ x ≤ 3 The solutions are all real numbers greater than and equal to – 11 and less than and equal to 3. GUIDED PRACTICE for Examples 5, 6 and 7 Solve the inequality. Then graph the solution. 11. x + 4 ≤ 9 or x – 3 ≥ 7 ANSWER x ≤ 5 or x ≥ 10 The graph is shown below. The solutions are all real numbers. less than or equal to 5 or greater than or equal to 10. GUIDED PRACTICE for Examples 5, 6 and 7 Solve the inequality. Then graph the solution. 12. 3 x – 1< – 1 or 2 x + 5 ≥ 11 ANSWER x < 0 or x ≥ 3 The graph is shown below. The solutions are all real numbers. less than 0 or greater than or equal to 3. 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. ANSWER 15 ≤ C ≤ 30 or 59 ≤ F ≤ 86