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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.