Over Lesson 1–6 1–5 5-Minute Check 1 Solve 3x + 7 > 22. Graph the solution set on a number line. {x | x > 5} Solve the inequality 3(3w + 1) ≥ 4.8. Graph the solution set on a number line. {w | w ≥ 0.2} Solve the inequality 7 + 3y > 4(y + 2). Graph the solution set on a number line.

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

Vocabulary compound inequality intersection union 2 inequalities joined by and or or

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

Concept

Example 1 Solve an “And” Compound Inequality Solve 10  3y – 2 < 19. Graph the solution set on a number line.

Concept

Example 2 Solve an “Or” Compound Inequality Solve x + 3 < 2 or –x  –4. Graph the solution set on a number line.

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

Example 3 Solve Absolute Value Inequalities A. Solve 2 > |d|. Graph the solution set on a number line.

Example 3 Solve Absolute Value Inequalities B. Solve 3 < |d|. Graph the solution set on a number line.

Concept

Example 4 Solve a Multi-Step Absolute Value Inequality Solve |2x – 2|  4. Graph the solution set on a number line.

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

Example 5 Write and Solve an Absolute Value Inequality A. JOB HUNTING To 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 The starting salary can differ from the average by as much as$2450. |38,500 – x|  2450

Example 5 Write and Solve an Absolute Value Inequality B. JOB HUNTING To 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

Example 5a A.|4.5 – w|  7 B.|w – 4.5|  7 C.|w – 7|  4.5 D.|7 – w|  4.5 A. HEALTH The average birth weight of a newborn baby is 7 pounds. However, this weight can vary by as much as 4.5 pounds. What is an absolute value inequality to describe this situation?

Example 5b A.{w | w ≤ 11.5} B.{w | w ≥ 2.5} C.{w | 2.5 ≤ w ≤ 11.5} D.{w | 4.5 ≤ w ≤ 7} B. HEALTH The average birth weight of a newborn baby is 7 pounds. However, this weight can vary by as much as 4.5 pounds. What is the range of birth weights for newborn babies?

Hwk: