Lesson 1.6: Solving Compound and Absolute Value Inequalities

Objectives:

• Solve Compound Inequalities • Solve Absolute Value Inequalities

Compound Inequalities

• Intersection --- “

AND

” • Solve the following compound inequality the graph the solution set on a number line.

10  3

y

• You can solve an intersection each side separately or you can solve and intersection both sides together.

Compound Inequalities

• Union --- “

OR

” • Solve the following compound inequality and the graph the solution set on a number line.

x x

4 • You must solve unions separately.

Quick Check:

• Solve the following compound inequalities and graph their solution sets on a number line.

4

y m

   

m

Absolute Value Inequalities

• Great”OR” Than --- creates an “OR”

c

.............

c

or

ax b c

• Less Than --- creates an “AND”

c

..........

c

Examples

• Solve the following inequalities and graph the solution set on a number line.

2

x

4 6

Quick Check

• Solve each inequality. Graph the solution set on a number line.

4

x

13 5

z

17 • Rachel is considering colleges to attend and determines that the average tuition among her choices is $3725 per year, but the tuition at a school could differ by as much as $1650 from the average. Write and solve an absolute value inequality to find the range of tuition.

Writing an Absolute Value Inequality From a Graph

Homework

• Page 45 and 46 --- 13 – 51 every other odd.

• Make sure you are studying for the Chapter 1 Test… practice tests and study guides are available on-line as well as in your book.

• Please read and take notes on Section 2.1 Relations and Functions for the day after the test.