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Then/Now

You solved one-step and multi-step inequalities. Solve compound inequalities. Solve absolute value inequalities. Then/Now. compound inequality. intersection union. Vocabulary. Concept. Solve an “And” Compound Inequality. Solve 10  3 y – 2 < 19. Graph the solution set on a number line.

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Then/Now

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  1. You solved one-step and multi-step inequalities. • Solve compound inequalities. • Solve absolute value inequalities. Then/Now

  2. compound inequality • intersection • union Vocabulary

  3. Concept

  4. Solve an “And” Compound Inequality Solve 10  3y – 2 < 19. Graph the solution set on a number line. Method 1 Solve separately. Write the compound inequality using the word and. Then solve each inequality. 10  3y – 2 and 3y – 2 < 19 12  3y 3y < 21 4  yy < 7 4  y < 7 Example 1

  5. Solve an “And” Compound Inequality Method 2 Solve both together. Solve both parts at the same time by adding 2 to each part. Then divide each part by 3. 10  3y – 2 < 19 12  3y < 21 4  y < 7 Example 1

  6. y 4 y< 7 4  y< 7 Solve an “And” Compound Inequality Graph the solution set for each inequality and find their intersection. Answer: Example 1

  7. y 4 y< 7 4  y< 7 Solve an “And” Compound Inequality Graph the solution set for each inequality and find their intersection. Answer: The solution set is y | 4  y < 7. Example 1

  8. A. B. C. D. What is the solution to 11  2x + 5 < 17? Example 1

  9. A. B. C. D. What is the solution to 11  2x + 5 < 17? Example 1

  10. Concept

  11. x  4 –x  –4 x + 3 < 2 x < –1 or x< –1 x 4 x < –1 or x 4 Solve an “Or” Compound Inequality Solve x + 3 < 2 or –x –4. Graph the solution set on a number line. Solve each inequality separately. Answer: Example 2

  12. x  4 –x  –4 x + 3 < 2 x < –1 or x< –1 x 4 x < –1 or x 4 Solve an “Or” Compound Inequality Solve x + 3 < 2 or –x –4. Graph the solution set on a number line. Solve each inequality separately. Answer: The solution set is x | x < –1 or x  4. Example 2

  13. A. B. C. D. What is the solution to x + 5 < 1 or –2x –6?Graph the solution set on a number line. Example 2

  14. A. B. C. D. What is the solution to x + 5 < 1 or –2x –6?Graph the solution set on a number line. Example 2

  15. Solve Absolute Value Inequalities A. Solve 2 > |d|. Graph the solution set on a number line. 2 > |d| means that the distance between d and 0 on a number line is less than 2 units. To make 2 > |d| true, you must substitute numbers for d that are fewer than 2 units from 0. Notice that the graph of 2 > |d| is the same as the graph of d > –2 and d < 2. All of the numbers between –2 and 2 are less than 2 units from 0. Answer: Example 3

  16. Solve Absolute Value Inequalities A. Solve 2 > |d|. Graph the solution set on a number line. 2 > |d| means that the distance between d and 0 on a number line is less than 2 units. To make 2 > |d| true, you must substitute numbers for d that are fewer than 2 units from 0. Notice that the graph of 2 > |d| is the same as the graph of d > –2 and d < 2. All of the numbers between –2 and 2 are less than 2 units from 0. Answer: The solution set is d | –2 < d < 2. Example 3

  17. A. B. C. D. A. What is the solution to |x| > 5? Example 3a

  18. A. B. C. D. A. What is the solution to |x| > 5? Example 3a

  19. A.{x | x > 5 or x < –5} B.{x | –5 < x < 5} C.{x | x < 5} D.{x | x > –5} B. What is the solution to |x| < 5? Example 3b

  20. A.{x | x > 5 or x < –5} B.{x | –5 < x < 5} C.{x | x < 5} D.{x | x > –5} B. What is the solution to |x| < 5? Example 3b

  21. Concept

  22. Solve a Multi-Step Absolute Value Inequality Solve |2x – 2|  4. Graph the solution set on a number line. |2x – 2|  4 is equivalent to 2x – 2  4 or 2x – 2  –4. Solve each inequality. 2x – 2  4 or 2x – 2  –4 2x  6 2x  –2 x  3 x  –1 Answer: Example 4

  23. Solve a Multi-Step Absolute Value Inequality Solve |2x – 2|  4. Graph the solution set on a number line. |2x – 2|  4 is equivalent to 2x – 2  4 or 2x – 2  –4. Solve each inequality. 2x – 2  4 or 2x – 2  –4 2x  6 2x  –2 x  3 x  –1 Answer: The solution set is x | x  –1 or x  3. Example 4

  24. A. B. C. D. What is the solution to |3x – 3| > 9? Graph the solution set on a number line. Example 4

  25. A. B. C. D. What is the solution to |3x – 3| > 9? Graph the solution set on a number line. Example 4

  26. The starting salary can differ from the average by as much as $2450. |38,500 – x|  2450 Write and Solve an Absolute Value Inequality A. JOB HUNTINGTo prepare for a job interview, Hinda researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ from the average by as much as $2450. Write an absolute value inequality to describe this situation. Let x = the actual starting salary. Answer: Example 5

  27. The starting salary can differ from the average by as much as $2450. |38,500 – x|  2450 Write and Solve an Absolute Value Inequality A. JOB HUNTINGTo prepare for a job interview, Hinda researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ from the average by as much as $2450. Write an absolute value inequality to describe this situation. Let x = the actual starting salary. Answer: |38,500 – x|  2450 Example 5

  28. Write and Solve an Absolute Value Inequality B. JOB HUNTINGTo prepare for a job interview, Hinda researches the position’s requirements and pay. She discovers that the average starting salary for the position is $38,500, but her actual starting salary could differ from the average by as much as $2450. Solve the inequality to find the range of Hinda’s starting salary. | 38,500 – x|  2450 Rewrite the absolute value inequality as a compound inequality. Then solve for x. –2450  38,500 – x  2450 –2450 – 38,500  –x  2450 – 38,500 –40,950  –x  –36,050 40,950  x  36,050 Example 5

  29. Write and Solve an Absolute Value Inequality Answer: Example 5

  30. Write and Solve an Absolute Value Inequality Answer: The solution set is x | 36,050  x  40,950.Hinda’s starting salary will fall within $36,050 and $40,950. Example 5

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