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Then/NowYou solved one-step and multi-step inequalities.Solve compound inequalities.Solve absolute value inequalities.

Vocabularycompound inequalityintersectionunion

Concept

Example 1Solve an And Compound InequalitySolve 10 3y 2 < 19. Graph the solution set on a number line.Method 1Solve separately.Write the compound inequality using the word and. Then solve each inequality.103y 2and3y 2 < 19123y3y < 21 4y y < 74 y < 7

Example 1Solve an And Compound InequalityMethod 2Solve both together.Solve both parts at the same time by adding 2 to each part. Then divide each part by 3.10 3y 2< 1912 3y< 214 y< 7

Example 1Solve an And Compound InequalityGraph the solution set for each inequality and find their intersection.Answer:

Example 1Solve an And Compound InequalityGraph the solution set for each inequality and find their intersection.Answer: The solution set is y | 4 y < 7.

Example 1What is the solution to 11 2x + 5 < 17?

Example 1What is the solution to 11 2x + 5 < 17?

Concept

Example 2Solve an Or Compound InequalitySolve x + 3 < 2 or x 4. Graph the solution set on a number line.Answer: Solve each inequality separately.

Example 2Solve an Or Compound InequalitySolve x + 3 < 2 or x 4. Graph the solution set on a number line.Answer: The solution set is x | x < 1 or x 4.Solve each inequality separately.

Example 2What is the solution to x + 5 < 1 or 2x 6? Graph the solution set on a number line.

Example 2What is the solution to x + 5 < 1 or 2x 6? Graph the solution set on a number line.

Example 3Solve Absolute Value InequalitiesA. 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.Answer: All of the numbers between 2 and 2 are less than 2 units from 0.Notice that the graph of 2 > |d| is the same as the graph of d > 2 and d < 2.

Example 3Solve Absolute Value InequalitiesA. 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.Answer: The solution set is d | 2 < d < 2.All of the numbers between 2 and 2 are less than 2 units from 0.Notice that the graph of 2 > |d| is the same as the graph of d > 2 and d < 2.

Example 3aA. What is the solution to |x| > 5?

Example 3aA. What is the solution to |x| > 5?

Example 3bB. What is the solution to |x| < 5?

Example 3bB. What is the solution to |x| < 5?

Concept

Example 4Solve a Multi-Step Absolute Value InequalitySolve |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 24or2x 242x62x2x3x1Answer:

Example 4Solve a Multi-Step Absolute Value InequalitySolve |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 24or2x 242x62x2x3x1Answer: The solution set is x | x 1 or x 3.

Example 4What is the solution to |3x 3| > 9? Graph the solution set on a number line.

Example 4What is the solution to |3x 3| > 9? Graph the solution set on a number line.

Example 5Write and Solve an Absolute Value InequalityA. JOB HUNTING To prepare for a job interview, Hinda researches the positions 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 5Write and Solve an Absolute Value InequalityA. JOB HUNTING To prepare for a job interview, Hinda researches the positions 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 5Write and Solve an Absolute Value InequalityB. JOB HUNTING To prepare for a job interview, Hinda researches the positions 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 Hindas starting salary. | 38,500 x | 2450Rewrite the absolute value inequality as a compound inequality. Then solve for x.245038,500 x 24502450 38,500x 2450 38,50040,950x 36,05040,950x 36,050

Example 5Write and Solve an Absolute Value InequalityAnswer:

Example 5Write and Solve an Absolute Value InequalityAnswer: The solution set is x | 36,050 x 40,950. Hindas starting salary will fall within $36,050 and $40,950.