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Solving Two-Step and Multi-Step Inequalities. 3-4. Holt Algebra 1. Warm Up. Lesson Presentation. Lesson Quiz. Warmup. Solve each inequality and graph the solutions. 1. 8 x < –24. x < –3. 2. –5 x ≥ 30. x ≤ – 6. 4. 3. x > 20. x ≥ 6.

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  1. Solving Two-Step and Multi-Step Inequalities 3-4 Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

  2. Warmup Solve each inequality and graph the solutions. 1. 8x < –24 x < –3 2. –5x ≥30 x ≤ –6 4. 3. x > 20 x ≥ 6 5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible number of shirts she can buy? 0, 1, 2, 3, 4, 5, 6, or 7 shirts

  3. Quiz – Start NOW Warmup

  4. Warm Up Solve each equation. 1. 2x – 5 = –17 2. –6 14 Solve each inequality and graph the solutions. t > –4 3. 5 < t + 9 4. a ≤ –8

  5. Objective Solve inequalities that contain more than one operation.

  6. Inequalities that contain more than one operation require more than one step to solve. Use inverse operations to undo the operations in the inequality one at a time.

  7. 45 + 2b > 61 –45 –45 b > 8 0 2 4 6 8 10 14 20 12 18 16 Example 1A: Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 45 + 2b > 61 Since 45 is added to 2b, subtract 45 from both sides to undo the addition. 2b > 16 Since b is multiplied by 2, divide both sides by 2 to undo the multiplication.

  8. 8 – 3y ≥ 29 –8 –8 –7 –8 –10 –6 –4 0 2 4 6 8 10 –2 Example 1B: Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 8 – 3y ≥ 29 Since 8 is added to –3y, subtract 8 from both sides to undo the addition. –3y ≥21 Since y is multiplied by –3, divide both sides by –3 to undo the multiplication. Change ≥ to ≤. y ≤ –7

  9. To solve more complicated inequalities, you may first need to simplify the expressions on one or both sides by using the order of operations, combining like terms, or using the Distributive Property.

  10. 10 –8 –10 –6 –4 0 2 4 6 8 –2 –3 Example 2A: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. 2 – (–10) > –4t 12 > –4t Combine like terms. Since t is multiplied by –4, divide both sides by –4 to undo the multiplication. Change > to <. –3 < t (or t > –3)

  11. –8 + 4x ≤ 8 +8 +8 10 –8 –10 –6 –4 0 2 4 6 8 –2 Example 2B: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. –4(2 – x) ≤ 8 −4(2 – x) ≤ 8 Distribute –4 on the left side. −4(2) − 4(−x) ≤ 8 Since –8 is added to 4x, add 8 to both sides. 4x ≤16 Since x is multiplied by 4, divide both sides by 4 to undo the multiplication. x ≤ 4

  12. –3 –3 Example 2C: Simplifying Before Solving Inequalities Solve the inequality and graph the solutions. Multiply both sides by 6, the LCD of the fractions. Distribute 6 on the left side. 4f + 3 > 2 Since 3 is added to 4f, subtract 3 from both sides to undo the addition. 4f > –1

  13. 0 Example 2C Continued 4f > –1 Since f is multiplied by 4, divide both sides by 4 to undo the multiplication.

  14. daily cost at We Got Wheels Cost at Rent-A-Ride must be less than $0.20 per mile # of miles. plus times 55 < 38 m + 0.20  Example 3: Application To rent a certain vehicle, Rent-A-Ride charges $55.00 per day with unlimited miles. The cost of renting a similar vehicle at We Got Wheels is $38.00 per day plus $0.20 per mile. For what number of miles in the cost at Rent-A-Ride less than the cost at We Got Wheels? Let m represent the number of miles. The cost for Rent-A-Ride should be less than that of We Got Wheels.

  15. 55 < 38 + 0.20m –38 –38 Example 3 Continued 55 < 38 + 0.20m Since 38 is added to 0.20m, subtract 8 from both sides to undo the addition. 17 < 0.20m Since m is multiplied by 0.20, divide both sides by 0.20 to undo the multiplication. 85 < m Rent-A-Ride costs less when the number of miles is more than 85.

  16. Check a number greater than 85. Check the endpoint, 85. 55 = 38 + 0.20m 55 < 38 + 0.20m 55 38 + 0.20(85) 55 < 38 + 0.20(90) 55 38 + 17 55 < 38 + 18  55 55  55 < 56 Example 3 Continued Check

  17. L3-4 pg 191 #18-72x3, add #37, 83 Assignment:

  18. Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. 13 – 2x ≥ 21 x ≤–4 2. –11 + 2 < 3p p > –3 t > 7 3. 23 < –2(3 –t) 4.

  19. Lesson Quiz: Part II 5. A video store has two movie rental plans. Plan A includes a $25 membership fee plus $1.25 for each movie rental. Plan B costs $40 for unlimited movie rentals. For what number of movie rentals is plan B less than plan A? more than 12 movies

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