Graph |x+16|<8

Math
|x+16|<8
Write |x+16|<8 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+16≥0
Subtract 16 from both sides of the inequality.
x≥-16
In the piece where x+16 is non-negative, remove the absolute value.
x+16<8
To find the interval for the second piece, find where the inside of the absolute value is negative.
x+16<0
Subtract 16 from both sides of the inequality.
x<-16
In the piece where x+16 is negative, remove the absolute value and multiply by -1.
-(x+16)<8
Write as a piecewise.
{x+16<8x≥-16-(x+16)<8x<-16
Simplify -(x+16)<8.
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Apply the distributive property.
{x+16<8x≥-16-x-1⋅16<8x<-16
Multiply -1 by 16.
{x+16<8x≥-16-x-16<8x<-16
{x+16<8x≥-16-x-16<8x<-16
{x+16<8x≥-16-x-16<8x<-16
Solve x+16<8 when x≥-16.
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Move all terms not containing x to the right side of the inequality.
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Subtract 16 from both sides of the inequality.
x<8-16
Subtract 16 from 8.
x<-8
x<-8
Find the intersection of x<-8 and x≥-16.
-16≤x<-8
-16≤x<-8
Solve -x-16<8 when x<-16.
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Solve -x-16<8 for x.
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Move all terms not containing x to the right side of the inequality.
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Add 16 to both sides of the inequality.
-x<8+16
Add 8 and 16.
-x<24
-x<24
Multiply each term in -x<24 by -1
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Multiply each term in -x<24 by -1. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
(-x)⋅-1>24⋅-1
Multiply (-x)⋅-1.
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Multiply -1 by -1.
1x>24⋅-1
Multiply x by 1.
x>24⋅-1
x>24⋅-1
Multiply 24 by -1.
x>-24
x>-24
x>-24
Find the intersection of x>-24 and x<-16.
-24<x<-16
-24<x<-16
Find the union of the solutions.
-24<x<-8
<div data-graph-input="{"graphs":[{"ascii":"-24<x
Graph |x+16|<8

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