Page 693 - Algebra 1

L E S S O N Solving Multi-Step Absolute-Value
101
Inequalities
Warm Up
New Concepts
1. Vocabulary A(n)
is a mathematical statement comparing
3. ⎢2 · -6 + 14 (7)
5. -5x + 12 ≥ 37 (77)
(45)
Simplify.
2. ⎢-8 + 5 - 7
(7)
Solve.
4. 3x - 7 > 17
(77)
quantities that are not equal.
Recall that an absolute-value inequality is solved by first isolating the absolute-value expression. Then the inequality is written as a compound inequality with no absolute-value symbols. The compound inequality uses AND when the absolute-value inequality is a “less than” inequality. The compound inequality uses OR when the absolute-value inequality is a “greater than” inequality.
Solving Multi-Step Absolute-Value Inequalities
Solve and graph each inequality.
a. 2⎢x +3<11
SOLUTION
Isolate ⎢x and then write the inequality as a compound inequality. 2⎢x + 3 < 11
Caution
The absolute-value expression must be isolated to apply the rules:
AND “less than” OR “greater than”
Example
1
Online Connection www.SaxonMathResources.com
The compound inequality can also be written as -4 < x < 4.
-6 -4 -2 0 2 4 6
-__3 -__3
2⎢x <8
2⎢x <8 __
22
⎢x <4
x > -4 and x < 4
Subtraction Property of Inequality Combine like terms.
Division Property of Inequality
Simplify.
Write as a compound inequality.
678 Saxon Algebra 1