Warm Ups 1/11

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# Warm Ups 1/11 - PowerPoint PPT Presentation

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 &lt; 135.

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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

### Chapter 5.3 Notes

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
• Solve: 6x + 3(2 – x) > -2x + 1
• Solve: 3x – 2(x – 4) < x – (2 – 3x)
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

Solving Compound Inequalities

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

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)
• 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

Solve -3 < x – 2 < 5

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

and

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

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)
• 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.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

4k – 7 ≤ 25 or 12 – 9k≥ 30

• Solve each inequality individually.

4k – 7 ≤ 25 or 12 – 9k≥ 30

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

Chapter 5.3

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

Chapter 5.4

Problems 6-17