Graph |x|-23>-10

Math
|x|-23>-10
Write |x|-23>-10 as a piecewise.
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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-23>-10
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-23>-10
Write as a piecewise.
{x-23>-10x≥0-x-23>-10x<0
{x-23>-10x≥0-x-23>-10x<0
Solve x-23>-10 when x≥0.
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Move all terms not containing x to the right side of the inequality.
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Add 23 to both sides of the inequality.
x>-10+23
Add -10 and 23.
x>13
x>13
Find the intersection of x>13 and x≥0.
x>13
x>13
Solve -x-23>-10 when x<0.
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Solve -x-23>-10 for x.
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Move all terms not containing x to the right side of the inequality.
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Add 23 to both sides of the inequality.
-x>-10+23
Add -10 and 23.
-x>13
-x>13
Multiply each term in -x>13 by -1
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Multiply each term in -x>13 by -1. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
(-x)⋅-1<13⋅-1
Multiply (-x)⋅-1.
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Multiply -1 by -1.
1x<13⋅-1
Multiply x by 1.
x<13⋅-1
x<13⋅-1
Multiply 13 by -1.
x<-13
x<-13
x<-13
Find the intersection of x<-13 and x<0.
x<-13
x<-13
Find the union of the solutions.
x<-13 or x>13
<div data-graph-input="{"graphs":[{"ascii":"x13","color":0,"isGrey":false,"dashed":false,"holes":[]}],"asymptotes":[],"segments":[],"areaBetweenCurves":[],"points":[],"HasGraphInput":true}” class=”GraphWrapper”>
Graph |x|-23>-10

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