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Mastering Inequalities: And, Or, Absolute Value - Math Review

Improve your math skills with compound inequalities, absolute value equations, and real-world problem-solving examples. Learn to solve complex equations step by step in this comprehensive lesson.

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Mastering Inequalities: And, Or, Absolute Value - Math Review

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 1–5) CCSS Then/Now New Vocabulary Key Concept: “And” Compound Inequalities Example 1: Solve an “And” Compound Inequality Key Concept: “Or” Compound Inequalities Example 2: Solve an “Or” Compound Inequality Example 3: Solve Absolute Value Inequalities Key Concept: Absolute Value Inequalities Example 4: Solve a Multi-Step Absolute Value Inequality Example 5: Real-World Example: Write and Solve an Absolute Value Inequality Lesson Menu

  3. A. {x | x > 5} B. {x | x < 5} C. {x | x > 6} D. {x | x < 6} Solve the inequality 3x + 7 > 22. Graph the solution set on a number line. 5-Minute Check 1

  4. A. {w | w ≤ 0.2} B. {w | w ≥ 0.2} C. {w | w ≥ 0.6} D. {w | w ≤ 0.6} Solve the inequality 3(3w + 1) ≥ 4.8. Graph the solution set on a number line. 5-Minute Check 2

  5. A. {y | y > 1} B. {y | y < 1} C. {y | y > –1} D. {y | y < –1} Solve the inequality 7 + 3y > 4(y + 2). Graph the solution set on a number line. 5-Minute Check 3

  6. Solve the inequality . Graph the solution set on a number line. A. {w | w ≤ –9} B. {w | w ≥ –9} C. {w | w ≤ –3} D. {w | w ≥ –3} 5-Minute Check 4

  7. Mathematical Practices 5 Use appropriate tools strategically. CCSS

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

  9. compound inequality • intersection • union Vocabulary

  10. Concept

  11. 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

  12. 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

  13. 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

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

  15. Concept

  16. 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

  17. 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

  18. 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

  19. Solve Absolute Value Inequalities B. Solve 3 < |d|. Graph the solution set on a number line. 3 < |d| means that the distance between d and 0 on a number line is greater than 3 units. To make 3 < |d| true, you must substitute values for d that are greater than 3 units from 0. Notice that the graph of 3 < |d| is the same as the graph of d < –3 or d > 3. All of the numbers not between –3 and 3 are greater than 3 units from 0. Answer: The solution set is d | d < –3 or d > 3. Example 3

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

  21. 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

  22. Concept

  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. End of the Lesson

  26. Pages 45 – 47 #12 – 16, 23, 28, 33,34, 37, 45, 50, 53

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