# Solve for x |x|>12 |x|>12
Write |x|>12 as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
x≥0
In the piece where x is non-negative, remove the absolute value.
x>12
To find the interval for the second piece, find where the inside of the absolute value is negative.
x<0
In the piece where x is negative, remove the absolute value and multiply by -1.
-x>12
Write as a piecewise.
{x>12x≥0-x>12x<0
{x>12x≥0-x>12x<0
Find the intersection of x>12 and x≥0.
x>12
Solve -x>12 when x<0.
Multiply each term in -x>12 by -1
Multiply each term in -x>12 by -1. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
(-x)⋅-1<12⋅-1
Multiply (-x)⋅-1.
Multiply -1 by -1.
1x<12⋅-1
Multiply x by 1.
x<12⋅-1
x<12⋅-1
Multiply 12 by -1.
x<-12
x<-12
Find the intersection of x<-12 and x<0.
x<-12
x<-12
Find the union of the solutions.
x<-12 or x>12
The result can be shown in multiple forms.
Inequality Form:
x<-12 or x>12
Interval Notation:
(-∞,-12)∪(12,∞)
<div data-graph-input="{"graphs":[{"ascii":"x12","color":0,"isGrey":false,"dashed":false,"holes":[]}],"asymptotes":[],"segments":[],"areaBetweenCurves":[],"points":[],"HasGraphInput":true}” class=”GraphWrapper”>
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