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Splash Screen. 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

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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. Evaluate the expression 5|xy – w| if w = –2, x = 1.5, and y = 4. A. 5 B. 10 C. 20 D. 40 5-Minute Check 3

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

  7. Solve the equation –4|a + 5| = –8. A. {7, 3} B. {2, 3} C. {–7, –3} D. {–2, 3} 5-Minute Check 5

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

  9. 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

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

  11. set-builder notation Vocabulary

  12. Concept

  13. 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

  14. 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

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

  16. Concept

  17. 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

  18. 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

  19. 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

  20. 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

  21. Solve Multi-Step Inequalities Example 3

  22. A. B. C. D. Example 3

  23. Write and Solve an Inequality CONSUMER COSTS Javier has at most $15.00 to spend today. He buys a bag of pretzels and a bottle of juice for $1.59. If gasoline at this store costs $2.89 per gallon, how many gallons of gasoline, to the nearest tenth of a gallon, can Javier buy for his car? Understand Let g = the number of gallons of gasoline that Javier buys. The total cost of the gasoline is 2.89g. The cost of the pretzels and juice plus the total cost of the gasoline must be less than or equal to $15.00. Example 4

  24. The cost ofpretzels & juice the costof gasoline is less thanor equal to $15.00. plus 1.59 + 2.89g 15.00 Write and Solve an Inequality Plan Write an inequality. Solve Original inequality Subtract 1.59 from each side. Simplify. Example 4

  25. Check Since is actually greater than 4.6,Javier will have enough money if he gets no more than 4.6 gallons of gasoline. Write and Solve an Inequality Divide each side by 2.89. Simplify. Answer: Javier can buy up to 4.6 gallons of gasoline for his car. Example 4

  26. RENTAL COSTSJeb wants to rent a car for his vacation. Value Cars rents cars for $25 per day plus $0.25 per mile. How far can he drive for one day if he wants to spend no more that $200 on car rental? A. up to 700 miles B. up to 800 miles C. more than 700 miles D. more than 800 miles Example 4

  27. End of the Lesson

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