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Warm Ups 1/11

Warm Ups 1/11. Marta wants to purchase charms for her necklace. Each charm costs $1.59. She wants to spend no more than $20 for the charms. Write an inequality to represent this situation? How many charms can Marta purchase ? Solve: -9 + 3x = 45 Solve AND Graph: -5x < 135.

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Warm Ups 1/11

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  1. Warm Ups 1/11 Marta wants to purchase charms for her necklace. Each charm costs $1.59. She wants to spend no more than $20 for the charms. Write an inequality to represent this situation? How many charms can Marta purchase? Solve: -9 + 3x = 45 Solve AND Graph: -5x < 135

  2. Chapter 5.3 Notes Solving Multi-Step Inequalities

  3. Solve like you would a multi-step equation… • Multi-Step Inequalities can be solved by undoing the operations the same way you would work to solve a Multi-Step Equation… Solve 13 – 11d = 79 Solve 13 – 11d > 79

  4. Examples… • Solve: -8x + 3 > -5 • Solve: 4n + 12 < n – 3

  5. Solving multi-step equations that involve the distributive property… • Solve: 6x + 3(2 – x) > -2x + 1

  6. Solving multi-step equations that involve the distributive property… • Solve: 3x – 2(x – 4) < x – (2 – 3x)

  7. Example… • Rob has a budget of $425 for senior pictures. The cost for a basic package and sitting fee is $200. He wants to buy extra wallet-size pictures for his friends that cost $4.50 each. How many wallet-size pictures can he order and stay within his budget?

  8. Chapter 5.4 Notes Solving Compound Inequalities

  9. New Vocabulary • Compound Inequality • Two or more inequalities that are connected by the words and or or. • Intersection • The graph of a compound inequality containing and; the solution is the set of elements common to both inequalities. • Union • The graph of a compound inequality containing or; the solution is a solution of either inequality, not necessarily both.

  10. Compound Inequality Ex: 1 Solve 7 < x + 2 < 11 • First express 7 < x + 2 < 11 using and. Then solve each individual inequality. 7 < x + 2 and x + 2 < 11

  11. Compound Inequality Ex: 1 (Continued) • Graph the solution by first graphing each individual answer…. • Then… Find where the answers intersect (or overlap)… this is your final answer!

  12. Compound Inequality Ex: 2 Solve -3 < x – 2 < 5 • First express 7 < x + 2 < 11 using and. Then solve each individual inequality. and

  13. Compound Inequality Ex: 2 (Continued) • Graph the solution by first graphing each individual answer…. • Then… Find where the answers intersect (or overlap)… this is your final answer!

  14. Compound Inequality Ex: 3 TRAVEL A ski resort has several types of hotel rooms and several types of cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount that a guest would pay per night at the resort.

  15. Compound Inequality Ex: 3 (Continued) • Graph the solution by first graphing each individual answer…. • Graph both solutions on the same number line. The solution represents a union.What do you notice???

  16. A.c ≤ 65or c ≥ 80 B.c ≥65or c ≤ 80 C.c ≥65or c ≥80 D.c ≤65or c ≤ 80 Compound Inequality Ex: 4 TICKET SALES A professional hockey arena has seats available in the Lower Bowl level that cost at most $65 per seat. The arena also has seats available at the Club Level and above that cost at least $80 per seat. Write and graph a compound inequality that describes the amount a spectator would pay for a seat at the hockey game.

  17. Compound Inequality Ex: 5 4k – 7 ≤ 25 or 12 – 9k≥ 30 • Solve each inequality individually. 4k – 7 ≤ 25 or 12 – 9k≥ 30

  18. Compound Inequality Ex: 5 (Continued) • Graph the solution by first graphing each individual answer…. • What do you notice about the answers??? Graph both solutions on the same number line.

  19. Homework… Due 1/15 Chapter 5.3 Problems 12-22, 24, 26, 28-31, 59 Chapter 5.4 Problems 6-17

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