---
title: Absolute Value
---
## Absolute Value

To say x absolute is to write it as |x|.
to say y absolute is to write it as |y|.
you get it.

Absolute Value Functions are very simple. They basically mean that whatever is in side the |?| will have a positive value.
Meaning |2| and |-2| both  are equal to 2. |3| and |-3| both are equal to 3. |x| and |-x| both are equal to x. Just follow the following problems to learn more.

Problem:- |x| = 5
From here take to roads. First road goes:-
Remove the absloute sign from the right side of the equation.
Equation becomes:-
x = 5 (solved)

The second road goes:-
Remove the absloute sign from the right side of the equation, and add a minus sign to the left side and make it look like this -("left side").
Equation becomes:-
x = -(5)
which is basically:-
x = -5 (solved)

So the solution is x = 5 or -5 (both 5 and -5 are the correct solutions because x can be either and absolute x will still be equal to 5)

The key words are the "right side" and the "left side".

Next Equation:-

Problem:-
2 + |x| = 5

First get x alone on one side:-
|x| = 5 - 2
|x| = 3

Now Road 1:-
|x| = 3
x = 3 (solved)

Road 2:-
|x| = 3
x = -(3)
x = -3

solution is:- x = 3 or -3.

Next equation:-
|x|^2 = 16

First get x alone on one side:-
|x| = sqroot(16)
|x| = 4


Now Road 1:-
|x| = 4
x = 4 (solved)

Road 2:-
|x| = 4
x = -(4)
x = -4

solution is:- x = 4 or -4


Now lets check for some logical fallacies in algebra problems:-

In absolute functions |x| will never equal a negetive number.
for example (the following problem is wrong, means it is not logically possible):-
|x| = -1
you can solve the problem but all solutions will be wrong because the problem itself is impossible.

So whenever you see an absolute |x| variable being equal to a negetive number just skip the problem or write down "the problem itself is impossible because absolute variables cannot be equal to negetive numbers".

Also absolute variables cannot be less then 0 so the problem " |x| < 0 " is also wrong ( logically impossible ).

Also when ever an absolute variable is equal to 0, that zero can be a double root in some cases.


The graph of absolute functions are just 2 straight lines. for example if x = 4 or -4 then there will be a stright vertical line at x = 4 and x=-4. 

This is a fast paced guide for absolute functions. more info is avalible from the web.