welcome to interactive chalkboard algebra 2 interactive chalkboard copyright © by the mcgraw-hill...

48
Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

Upload: frank-felix-jordan

Post on 20-Jan-2018

219 views

Category:

Documents


0 download

DESCRIPTION

Lesson 5 Contents Example 1Solve an Inequality Using Addition or Subtraction Example 2Solve an Inequality Using Multiplication or Division Example 3Solve a Multi-Step Inequality Example 4Write an Inequality

TRANSCRIPT

Page 1: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Algebra 2 Interactive ChalkboardCopyright © by The McGraw-Hill Companies, Inc.

Send all inquiries to:

GLENCOE DIVISIONGlencoe/McGraw-Hill8787 Orion PlaceColumbus, Ohio 43240

Page 2: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Lesson 1-5 Solving Inequalities

Lesson 1-6Solving Compound and Absolute Value Inequalities

Page 3: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Example 1Solve an Inequality Using Addition or Subtraction

Example 2Solve an Inequality Using Multiplicationor Division

Example 3 Solve a Multi-Step Inequality

Example 4 Write an Inequality

Page 4: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Solve Graph the solution set on a number line.

Original inequality

Subtract 4y from each side.

Simplify.

Subtract 2 from each side.

Simplify.

Rewrite with y first.

Page 5: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Answer: Any real number greater than –5 is a solution of this inequality.

A circle means that this point is not included in the solution set.

Page 6: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Answer:

Solve Graph the solution set on a number line.

Page 7: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Solve Graph the solution set on a number line.

–40 p Simplify.

p –40 Rewrite with p first.

Original inequality

Divide each side by –0.3, reversing the inequality symbol.

Page 8: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Answer: The solution set is

A dot means that this point is included in the solution set.

Page 9: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Solve Graph the solution set on a number line.

Answer:

Page 10: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Solve Graph the solution set on a

number line.

Original inequality

Multiply each side by 2.

Add –x to each side.

Divide each side by –3, reversing the inequality symbol.

Page 11: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Answer: The solution set is and is graphed below.

Page 12: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Solve Graph the solution set on a

number line.

Answer:

Page 13: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Consumer Costs Alida has at most $10.50 to spend at a convenience store. She buys a bag of potato chips and a can of soda for $1.55. If gasoline at this store costs $1.35 per gallon, how many gallons of gasoline can Alida buy for her car, to the nearest tenth of a gallon?

Explore Let the number of gallons of gasoline that Alida buys.

Plan The total cost of the gasoline is 1.35g. The cost of the chips and soda plus the total cost of the gasoline must be less than or equal to $10.50. Write an inequality.

Page 14: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

The cost ofchips & soda plus

the costof gasoline

is less thanor equal to $10.50.

1.55 + 1.35g 10.50

Divide each side by 1.35.

Solve Original inequality

Subtract 1.55 from each side.

Simplify.

Simplify.

Page 15: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Answer: Alida can buy up to 6.6 gallons of gasoline for her car.

Examine Since is actually greater than 6.6, Alida

will have enough money if she gets no more

than 6.6 gallons of gasoline.

Page 16: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Rental Costs Jeb wants to rent a car for his vacation. Value Cars rents cars for $25 per day plus $0.25 per mile. How far can he drive for one day if he wants to spend no more that $200 on car rental?

Answer: up to 700 miles

Page 17: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…
Page 18: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Example 1 Solve an “and” Compound Inequality

Example 2 Solve an “or” Compound Inequality

Example 3 Solve an Absolute Value Inequality (<)

Example 4 Solve an Absolute Value Inequality (>)

Example 5Solve a Multi-Step Absolute Value Inequality

Example 6 Write an Absolute Value Inequality

Page 19: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

SolveGraph the solution set on a number line.Method 1 Write the compound inequality using the word

and. Then solve each inequality.and

Method 2 Solve both parts at the same time by adding 2 to each part. Then divide each part by 3.

Page 20: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Graph the solution set for each inequality and find their intersection.

y 4

Page 21: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

SolveGraph the solution set on a number line.

Answer:

Page 22: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Solve each inequality separately.or

Answer: The solution set is

Solve orGraph the solution set on a number line.

Page 23: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Answer:

SolveGraph the solution set on a number line.

Page 24: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

You can interpret to mean that the distance between d and 0 on a number line is less than 3 units. To make true, you must substitute numbers for d that are fewer than 3 units from 0.

All of the numbers between –3 and 3 are less than 3 units from 0.

Solve Graph the solution set on a number line.

Answer: The solution set is

Notice that the graph of is the same as the graph of d > –3 and d < 3.

Page 25: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Answer:

Solve Graph the solution set on a number line.

Page 26: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

You can interpret to mean that the distance between d and 0 on a number line is greater than 3 units. To make true, you must substitute values for d that are greater than 3 units from 0.

All of the numbers not between –3 and 3 are greater than 3 units from 0.

Answer: The solution set is

Notice that the graph of is the same as the

graph of

Solve Graph the solution set on a number line.

Page 27: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Solve Graph the solution set on a number line.

Answer:

Page 28: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

SolveGraph the solution set on a number line.

Solve each inequality.

or

is equivalent to

Answer: The solution set is .

Page 29: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

SolveGraph the solution set on a number line.

Answer:

Page 30: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Housing According to a recent survey, the average monthly rent for a one-bedroom apartment in one city is $750. However, the actual rent for any given one-bedroom apartment might vary as much as $250 from the average.

Write an absolute value inequality to describe this situation.Let the actual monthly rent.

The rent for an apartmentcan differ from the average by as much as $250.

Answer: 250

Page 31: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Answer: The solution set isThe actual rent falls between $500 and $1000, inclusive.

Solve the inequality to find the range of monthly rent.Rewrite the absolute value inequality as a compound inequality. Then solve for r.

–rr

–r

Page 32: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Health The average birth weight of a newborn baby is 7 pounds. However, this weight can vary by as much as 4.5 pounds.

a. Write an absolute value inequality to describe this situation.

b. Solve the inequality to find the range of birth weights for newborn babies.

Answer:

Answer: The birth weight of anewborn baby will fall between 2.5 pounds and 11.5 pounds, inclusive.

Page 33: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…
Page 34: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Explore online information about the information introduced in this chapter.

Click on the Connect button to launch your browser and go to the Algebra 2 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.algebra2.com/extra_examples.

Page 35: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Page 36: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…
Page 37: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Page 38: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…
Page 39: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Page 40: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…
Page 41: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Page 42: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…
Page 43: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Page 44: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…
Page 45: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Page 46: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…
Page 47: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…

End of Custom ShowsWARNING! Do Not Remove

This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.

Page 48: Welcome to Interactive Chalkboard Algebra 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies,…