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Inequalities: Addition, Subtraction, Multiplication, and Division

Learn how to solve inequalities using addition, subtraction, multiplication, and division. Practice solving one-step and multi-step inequalities and graph the solution sets on a number line.

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Inequalities: Addition, Subtraction, Multiplication, and Division

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 1–4) CCSS Then/Now New Vocabulary Key Concept: Addition / Subtraction Property of Inequality Example 1: Solve an Inequality Using Addition or Subtraction Key Concept: Multiplication / Division Property of Inequality Example 2: Solve an Inequality Using Multiplication or Division Example 3: Solve Multi-Step Inequalities Example 4: Write and Solve an Inequality Lesson Menu

  3. Evaluate the expression |4w + 3| if w = –2. A. 5 B. 7 C. 11 D. 12 5-Minute Check 1

  4. Evaluate the expression |2x + y| if x = 1.5 and y = 4. A. 5 B. 7 C. 10 D. 20 5-Minute Check 2

  5. Solve the equation |b + 20| = 21. A. {–41, 1} B. {–41, –1} C. {–1, 1} D. {1, 2} 5-Minute Check 4

  6. A. B. C. D. What is the solution to the equation2|3x – 1| – 1 = –5? 5-Minute Check 6

  7. Content Standards A.CED.1 Create equations and inequalities in one variable and use them to solve problems. A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Mathematical Practices 4 Model with mathematics. CCSS

  8. You solved equations involving absolute values. • Solve one-step inequalities. • Solve multi-step inequalities. Then/Now

  9. set-builder notation Vocabulary

  10. Concept

  11. Solve an Inequality Using Addition or Subtraction Solve 4y – 3 < 5y + 2. Graph the solution set on a number line. 4y – 3 < 5y + 2 Original inequality 4y – 3 – 4y < 5y + 2 – 4y Subtract 4y from each side. –3 < y + 2 Simplify. –3 – 2 < y + 2 – 2 Subtract 2 from each side. –5 < y Simplify. y > –5 Rewrite with y first. Example 1

  12. A circle means that this point is not included in the solution set. Solve an Inequality Using Addition or Subtraction Answer: Any real number greater than –5 is a solution of this inequality. Example 1

  13. A. B. C. D. Which graph represents the solution to 6x – 2 < 5x + 7? Example 1

  14. Concept

  15. Solve an Inequality Using Multiplication or Division Solve 12  –0.3p. Graph the solution set on a number line. Original inequality Divide each side by –0.3, reversing the inequality symbol. Simplify. Rewrite with p first. Example 2

  16. A dot means that this point is included in the solution set. Solve an Inequality Using Multiplication or Division Answer: The solution set is p | p  –40. Example 2

  17. A. {x | x –7} B. {x | x –7} C. {x | x 7} D. {x | x 7} What is the solution to –3x 21? Example 2

  18. Solve Multi-Step Inequalities Original inequality Multiply each side by 2. Add –x to each side. Divide each side by –3, reversing the inequality symbol. Example 3

  19. Solve Multi-Step Inequalities Example 3

  20. A. B. C. D. Example 3

  21. End of the Lesson

  22. Pages 37 – 38 #10 – 18, 28, 29, 45, 54 - 56

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