# Graph |(x+2)/3|<1

|x+23|<1
Write |x+23|<1 as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
x+23≥0
Solve the inequality.
Multiply both sides of the equation by 3.
x+2≥0⋅(3)
Remove parentheses.
x+2≥0⋅(3)
Multiply 0 by 3.
x+2≥0
Subtract 2 from both sides of the inequality.
x≥-2
x≥-2
In the piece where x+23 is non-negative, remove the absolute value.
x+23<1
To find the interval for the second piece, find where the inside of the absolute value is negative.
x+23<0
Solve the inequality.
Multiply both sides of the equation by 3.
x+2<0⋅(3)
Remove parentheses.
x+2<0⋅(3)
Multiply 0 by 3.
x+2<0
Subtract 2 from both sides of the inequality.
x<-2
x<-2
In the piece where x+23 is negative, remove the absolute value and multiply by -1.
-x+23<1
Write as a piecewise.
{x+23<1x≥-2-x+23<1x<-2
{x+23<1x≥-2-x+23<1x<-2
Solve x+23<1 when x≥-2.
Solve x+23<1 for x.
Multiply both sides of the equation by 3.
x+2<1⋅(3)
Remove parentheses.
x+2<1⋅(3)
Multiply 3 by 1.
x+2<3
Move all terms not containing x to the right side of the inequality.
Subtract 2 from both sides of the inequality.
x<3-2
Subtract 2 from 3.
x<1
x<1
x<1
Find the intersection of x<1 and x≥-2.
-2≤x<1
-2≤x<1
Solve -x+23<1 when x<-2.
Solve -x+23<1 for x.
Multiply each term in -x+23<1 by -1
Multiply each term in -x+23<1 by -1. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
(-x+23)⋅-1>1⋅-1
Multiply (-x+23)⋅-1.
Multiply -1 by -1.
1x+23>1⋅-1
Multiply x+23 by 1.
x+23>1⋅-1
x+23>1⋅-1
Multiply -1 by 1.
x+23>-1
x+23>-1
Multiply both sides of the equation by 3.
x+2>-1⋅3
Remove parentheses.
x+2>-1⋅3
Multiply -1 by 3.
x+2>-3
Move all terms not containing x to the right side of the inequality.
Subtract 2 from both sides of the inequality.
x>-3-2
Subtract 2 from -3.
x>-5
x>-5
x>-5
Find the intersection of x>-5 and x<-2.
-5<x<-2
-5<x<-2
Find the union of the solutions.
-5<x<1
<div data-graph-input="{"graphs":[{"ascii":"-5<x
Graph |(x+2)/3|<1