Page 502 - Algebra 1

L E S S O N Solving Absolute-Value Equations 74
Warm Up
New Concepts
1. Vocabulary The of a number n is the distance from n to 0 on
(5)
Solve. 2.-5m+6=8
(23)
4. 3m - 7m = 8m - 6 (28)
a number line.
3._2x-_3 =_1 (23) 5 10 2
5. -m - 6m + 4 = -2m - 5 (28)
The absolute value of a number n is the distance from n to 0 on a number line. ⎪-5⎥ = 5 ⎪7⎥ = 7
5 units 7 units
-8 -6 -4 -2 0 2 4 6 8
An equation that has one or more absolute-value expressions is called an absolute-value equation. There are two numeric values for x that have an absolute value of 5.
If |x| = 5, then x = 5 or x = -5. ⎪-5⎥ = 5 ⎪5⎥ = 5
5 units 5 units
-8 -6 -4 -2 0 2 4 6 8 solution set: {5, -5}
In the equation |x + 2| = 6, |x + 2| represents a distance of 6 units from
the origin. The two numeric values for (x + 2) that have an absolute value of 6 are 6 and -6.
If |x + 2| = 6, then (x + 2) = 6 or (x + 2) = –6. x = -8
units
-8 -6 -4 -2 0 2 4 6 8
6 units 6 units ⎪x+2⎥ =6 ⎪x+2⎥ =6
solution set: {4, -8}
Math Reasoning
Verify Use the definition of absolute value to verify that the absolute value of a number is never negative.
x=4 +2 units
Online Connection www.SaxonMathResources.com
Lesson 74 487