Page 504 - Algebra 1

b. 4⎢x-2 =80 SOLUTION
Isolate the absolute value.
4⎪x-2 = 80 __
Division Property of Equality ⎪x - 2 = 20 Simplify.
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Write ⎢x - 2 = 20 as two equations.
x - 2 = 20 or
x = 22 Add 2 to both sides.
The solution is {22, -18}. Check
4⎪x - 2 = 80 4⎪x - 2 4⎪22-2 80 4⎪-18 - 2 4⎪20 80 4⎪-20 4 · 20 80 4 · 20 80 = 80 80
x - 2 = -20 x = -18
=80 80 80 80 =80
Solving Special Cases
Example
3
Solve.
a. ⎢x-6 -2=-2 SOLUTION
Isolate the absolute value. ⎢x - 6 - 2 = -2
⎢x - 6 = 0 Add 2 to both sides.
The absolute-value equation can be written as one equation: (x - 6) = 0.
x-6=0 x=6
The equation has only one solution. The solution is {6}.
b. ⎢x + 4 = -8 SOLUTION
The expression ⎪x + 4 is equal to a negative value. Absolute value is a distance from 0, so it cannot be equal to a negative number. There is no solution. The solution is written as {} or Ø, meaning that the solution set is empty.
Math Reasoning
Analyze Why does the absolute-value equation ⎢x - 6 = 0 have only one solution?
Lesson 74 489