Warm Up

1
Solve Absolute Value Inequalities
Warm Up
Lesson Presentation
Lesson Quiz
2
Warm-Up
1. Solve x 6 4.
2. Solve x 5 8 2.
3. A frame will hold photographs that are 5
inches by 8 inches with an absolute derivation
of 0.25 inch for length and width. What are the
minimum and maximum dimensions for photos?
3
Example 1
Solve the inequality. Graph your solution.
x ? 6
a.
SOLUTION
4
Example 1
SOLUTION
The distance between x and 0 is less than or
equal to 0.5. So, 0.5 x 0.5.
5
Guided Practice
Solve the inequality. Graph your solution.
1. x ? 8
2. u lt 3.5
6
Example 2
Write original inequality.
Rewrite as compound inequality.
Add 5 to each side.
7
Example 3
Solve 4x 5 3 lt 9. Graph your solution.
4x 5 3 lt 9
Write original inequality.
4x 5 lt 6
Subtract 3 from each side.
6 lt 4x 5 lt 6
Rewrite as compound inequality.
1 lt 4x lt 11
Add 5 to each expression.
0.25 gt x gt 2.75
Divide each expression by 4. Reverse inequality
symbol.
2.75 lt x lt 0.25
Rewrite in the form a lt x lt b.
8
Example 3
9
Guided Practice
Solve the inequality. Graph your solution.
10
Guided Practice
Solve the inequality. Graph your solution.
11
Example 4
Computers
You are buying a new computer and find 10 models
in a store advertisement. The prices are 890,
750, 650, 370, 660, 670, 450, 650,
725, and 825.
12
Example 4
SOLUTION
STEP 1
Find the mean by dividing the sum of the prices
by 10.
664
13
Example 4
STEP 2
Write absolute value inequality.
100 x 664 100
Write as compound inequality.
564 x 764
Add 664 to each expression.
14
Guided Practice
7. WHAT IF? In Example 4, suppose that you are
willing to pay the mean price with an absolute
deviation of at most 75. How many of the
computer prices meet this condition?
15
Lesson Quiz
Solve the inequality. Graph your solution.
1. x 5 gt 3
2. x 3 6 ? 8
16
Lesson Quiz