Chapter 1Section 1.7

Yesterday’s Exit SlipO Draw a graph that shows the solution set (x| x > -2)

O Write half of five times a number is less than equal to 10 as an inequality.

(5x) 10O 6 > 3 6>-3 -6<3 -6<-3

Divide each side of each inequality above by 2. Record each result. Are the inequalities the same?

Yes O 6 > 3 6>-3 -6<3 -6<-3

Divide each side of each inequality above by -2. Record each result. Are the inequalities the same?

-3 > -3/2 -3>-3/2 3<-3/23<3/2

No, when you multiple by a negative number, the inequality must by reversed.

-2

Objectives:O To solve compound inequalities using

and and or.O To solve inequalities involving

absolute value and graph the solutions.

Why do we need this?

You can use absolute value inequalities to solve problems involving entertainment and education.

Compound InequalitiesA compound inequality is an equation with two or more inequalities joined together with either "and" or "or“.

AND means intersection-what do the two items

have in common?

OR means union-if it is in one item, it is

in the solution

A

A B

B

ExampleGraph x < 4 and x ≥ 2

a) Graph x < 4

b) Graph x ≥ 2

c) Combine the graphsd) Where do they intersect?

3 42o

3 42●

●3 42

o

ExampleGraph x < 2 or x ≥ 4

a) Graph x < 2

3 42o

b) Graph x ≥ 4

3 42●

c) Combine the graphs

3 42o ●

Example

Solve and Graph: 9 < 3x + 6 < 15

9 < 3x + 6 < 15

9 < 3x + 6

3x + 6 < 15

1 < x x < 3

0 1 3

1< x < 3

Solving Absolute Value Inequality

Why do you think we need to review compound inequalities before continuing with absolute value inequalities?

Example

Solve and Graph: |2x + 4| 12

|2x + 4| 12

2x + 4 12 2x + 4 -12

2x 8x 4

2x -16

x -8

0 4-8

greatOR

ororor

Example

Solve and Graph: |x - 3| < 2

|x - 3| < 2

x -3 < 2 x – 3 > -2

x < 5 x > -2

0 5-2

less

thand

and

and

Writing Absolute Value Inequalities

You work in the quality control department of a manufacturing company. The diameter of a drill bit must be between 0.62 inch and 0.63 inch. Write an absolute-value inequality to represent this requirement.

How do we solve this?

SolutionLet d represent the diameter (in inches) of the drill bit.O Write a compound inequality.

O Find the halfway point.

O Subtract 0.625 from each part of the compound inequality.

O Rewrite as an absolute-value inequality.

0.62 ≤ d ≤ 0.63

0.625

0.62 - 0.625 ≤ d - 0.625 ≤ 0.63 - 0.625

-0.005 ≤ d - 0.625 ≤ 0.005

|d - 0.625|≤ 0.005

Mid-Exit tickets

These were our objectives:O To solve compound inequalities using

and and or.O To solve inequalities involving

absolute value and graph the solutions.

Keep these in mind while answering your questions.