101 lines
2.3 KiB
Markdown
101 lines
2.3 KiB
Markdown
---
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title: Absolute Value
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---
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## Absolute Value
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To say x absolute is to write it as |x|.
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to say y absolute is to write it as |y|.
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you get it.
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Absolute Value Functions are very simple. They basically mean that whatever is in side the |?| will have a positive value.
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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.
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Problem:- |x| = 5
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From here take to roads. First road goes:-
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Remove the absloute sign from the right side of the equation.
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Equation becomes:-
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x = 5 (solved)
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The second road goes:-
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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").
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Equation becomes:-
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x = -(5)
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which is basically:-
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x = -5 (solved)
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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)
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The key words are the "right side" and the "left side".
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Next Equation:-
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Problem:-
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2 + |x| = 5
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First get x alone on one side:-
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|x| = 5 - 2
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|x| = 3
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Now Road 1:-
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|x| = 3
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x = 3 (solved)
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Road 2:-
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|x| = 3
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x = -(3)
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x = -3
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solution is:- x = 3 or -3.
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Next equation:-
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|x|^2 = 16
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First get x alone on one side:-
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|x| = sqroot(16)
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|x| = 4
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Now Road 1:-
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|x| = 4
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x = 4 (solved)
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Road 2:-
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|x| = 4
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x = -(4)
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x = -4
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solution is:- x = 4 or -4
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Now lets check for some logical fallacies in algebra problems:-
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In absolute functions |x| will never equal a negetive number.
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for example (the following problem is wrong, means it is not logically possible):-
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|x| = -1
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you can solve the problem but all solutions will be wrong because the problem itself is impossible.
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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".
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Also absolute variables cannot be less then 0 so the problem " |x| < 0 " is also wrong ( logically impossible ).
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Also when ever an absolute variable is equal to 0, that zero can be a double root in some cases.
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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.
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This is a fast paced guide for absolute functions. more info is avalible from the web.
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