The absolute value of x is written as \displaystyle |x|∣x∣. It has the following properties:
If
x
≥
0
,
then
|
x
|
=
x
.
If
x
<
0
,
then
|
x
|
=
−
x
.
For real numbers \displaystyle AA and \displaystyle BB, an equation of the form \displaystyle |A|=B∣A∣=B, with \displaystyle B\ge 0B≥0, will have solutions when \displaystyle A=BA=B or \displaystyle A=-BA=−B. If \displaystyle B<0B<0, the equation \displaystyle |A|=B∣A∣=B has no solution.
