Page 639 - Algebra 1

L E S S O N Solving Multi-Step Absolute-Value Equations 94
Warm Up
New Concepts
1. Vocabulary The of a number n is the distance from n to 0 on a
(5)
Simplify.
2. ⎪-9⎥ - 5
(5)
Solve.
4. 6x - 7 = 11
(26)
number line.
3. ⎪12 - 23⎥ (5)
5. 11x + 8 = 41 (26)
To solve an absolute-value equation, begin by isolating the absolute value. Then use the definition of absolute value to write the absolute-value equation as two equations. Solve each equation, and write the solution set. There are often two answers to an absolute-value equation. The solutions can be graphed on a number line by placing a closed circle at each value in the solution set.
Solving Equations with Two Operations
Solve each equation. Then graph the solution.
_
a. ⎪x⎥+3=18
5
SOLUTION
First isolate the absolute value. Write the equation so that the absolute value is on one side of the equation by itself.
Subtraction Property of Equality Simplify.
Multiplication Property of Equality
Simplify.
Write as two equations without an absolute value.
Math Language
The absolute value of a number n is the distance from 0 to n on a number line. The absolute value of 0 is 0.
Example
1
Hint
Isolate the absolute value using inverse operations.
⎪x⎥ _
5 +3=18 -__3 = -__3
_
⎪x⎥ = 15
5 _
5 · ⎪x⎥ = 5 · 15 5
⎪x⎥ = 75
x = 75 or x = -75
Online Connection www.SaxonMathResources.com
The solution set is {-75, 75}.
Graph the solution on a number line.
-75 -50 -25 0 25 50 75
624 Saxon Algebra 1