Page 640 - Algebra 1

b. 4⎪x⎥-9=15
SOLUTION
First isolate the absolute value.
4⎪x⎥ - 9 = 15 4⎪x⎥ = 24
⎪x⎥ = 6 x = 6 and
Add 9 to both sides.
Divide both sides by 4.
Write as two equations without an absolute value.
x = -6
The solution set is {-6, 6}.
Graph the solution on a number line.
-6 -4 -2 0 2 4 6
Solving Equations with More than Two Operations
Example
2
Solve each equation. _
Math Reasoning
Analyze Why can the absolute value never be negative?
a. 5⎪x⎥+4=4 2
SOLUTION
_
5⎪x⎥ +4=4
2_
5⎪x⎥ = 0
Subtract 4 from both sides.
Multiply both sides by 2. Divide both sides by 5.
2
5⎪x⎥ = 0
⎪x⎥ = 0
Since the absolute value is equal to zero, there is only one solution. The
solution set is {0}. _
b. 2⎪x⎥+3=1 6
SOLUTION
_
2⎪x⎥ +3=1
6
2⎪x⎥ = -2 _
6
2⎪x⎥ = -12
⎪x⎥ = -6
Subtract 3 from both sides.
Multiply both sides by 6. Divide both sides by 2.
By the definition of absolute value, we know that there are no solutions to this equation. The absolute value is never negative. The solution set is empty. You can write this as {} or Ø.
Lesson 94 625