# Graph |x-2|<5

|x-2|<5
Write |x-2|<5 as a piecewise.
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
x-2≥0
Add 2 to both sides of the inequality.
x≥2
In the piece where x-2 is non-negative, remove the absolute value.
x-2<5
To find the interval for the second piece, find where the inside of the absolute value is negative.
x-2<0
Add 2 to both sides of the inequality.
x<2
In the piece where x-2 is negative, remove the absolute value and multiply by -1.
-(x-2)<5
Write as a piecewise.
{x-2<5x≥2-(x-2)<5x<2
Simplify -(x-2)<5.
Apply the distributive property.
{x-2<5x≥2-x–2<5x<2
Multiply -1 by -2.
{x-2<5x≥2-x+2<5x<2
{x-2<5x≥2-x+2<5x<2
{x-2<5x≥2-x+2<5x<2
Solve x-2<5 when x≥2.
Move all terms not containing x to the right side of the inequality.
Add 2 to both sides of the inequality.
x<5+2
Add 5 and 2.
x<7
x<7
Find the intersection of x<7 and x≥2.
2≤x<7
2≤x<7
Solve -x+2<5 when x<2.
Solve -x+2<5 for x.
Move all terms not containing x to the right side of the inequality.
Subtract 2 from both sides of the inequality.
-x<5-2
Subtract 2 from 5.
-x<3
-x<3
Multiply each term in -x<3 by -1
Multiply each term in -x<3 by -1. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
(-x)⋅-1>3⋅-1
Multiply (-x)⋅-1.
Multiply -1 by -1.
1x>3⋅-1
Multiply x by 1.
x>3⋅-1
x>3⋅-1
Multiply 3 by -1.
x>-3
x>-3
x>-3
Find the intersection of x>-3 and x<2.
-3<x<2
-3<x<2
Find the union of the solutions.
-3<x<7
<div data-graph-input="{"graphs":[{"ascii":"-3<x
Graph |x-2|<5

Scroll to top