|x|-23>-10

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

Move all terms not containing x to the right side of the inequality.

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 for x.

Move all terms not containing x to the right side of the inequality.

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

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.

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”>