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### Chapter 5.3 Notes

### Chapter 5.4 Notes property…

### Homework… Due 1/15 property…

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

Solving Multi-Step Inequalities

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

Examples…

- Solve: -8x + 3 > -5
- Solve: 4n + 12 < n – 3

Solving multi-step equations that involve the distributive property…

- Solve: 6x + 3(2 – x) > -2x + 1

Solving multi-step equations that involve the distributive property…

- Solve: 3x – 2(x – 4) < x – (2 – 3x)

Example… property…

- 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?

Solving Compound Inequalities

New Vocabulary property…

- 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 property…

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

Compound Inequality Ex: 1 (Continued) property…

- 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 property…

Solve -3 < x – 2 < 5

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

Compound Inequality Ex: 2 (Continued) property…

- 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 property…

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) property…

- 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???

A. property…c ≤ 65or c ≥ 80

B.c ≥65or c ≤ 80

C.c ≥65or c ≥80

D.c ≤65or c ≤ 80

Compound Inequality Ex: 4TICKET 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 property…

4k – 7 ≤ 25 or 12 – 9k≥ 30

- Solve each inequality individually.
4k – 7 ≤ 25 or 12 – 9k≥ 30

Compound Inequality Ex: 5 (Continued) property…

- Graph the solution by first graphing each individual answer….
- What do you notice about the answers??? Graph both solutions on the same number line.

Chapter 5.3

Problems 12-22, 24, 26, 28-31, 59

Chapter 5.4

Problems 6-17

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