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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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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


Chapter 5 3 notes

Chapter 5.3 Notes

Solving Multi-Step Inequalities


Solve like you would a multi step equation

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 = 79Solve 13 – 11d > 79


Examples

Examples…

  • Solve: -8x + 3 > -5

  • Solve: 4n + 12 < n – 3


Solving multi step equations that involve the distributive property

Solving multi-step equations that involve the distributive property…

  • Solve: 6x + 3(2 – x) > -2x + 1


Solving multi step equations that involve the distributive property1

Solving multi-step equations that involve the distributive property…

  • Solve: 3x – 2(x – 4) < x – (2 – 3x)


Example

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?


Chapter 5 4 notes

Chapter 5.4 Notes

Solving Compound Inequalities


New vocabulary

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.


Compound inequality ex 1

Compound Inequality Ex: 1

Solve 7 < x + 2 < 11

  • First express 7 < x + 2 < 11 using and. Then solve each individual inequality.

    7 < x + 2and x + 2 < 11


Compound inequality ex 1 continued

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!


Compound inequality ex 2

Compound Inequality Ex: 2

Solve -3 < x – 2 < 5

  • First express 7 < x + 2 < 11 using and. Then solve each individual inequality.

    and


Compound inequality ex 2 continued

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!


Compound inequality ex 3

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.


Compound inequality ex 3 continued

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???


Compound inequality ex 4

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.


Compound inequality ex 5

Compound Inequality Ex: 5

4k – 7 ≤ 25 or 12 – 9k≥ 30

  • Solve each inequality individually.

    4k – 7 ≤ 25 or 12 – 9k≥ 30


Compound inequality ex 5 continued

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.


Homework due 1 15

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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