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    (Original post by man111111)
    why do you multiply x-2 with -1
    By definition of |x| we have |x-2| = 2-x for x < 2. Clearly, when you're talking about the interval 0<x<1 this is just a subinterval of x<2.

    Otherwise, you can just sketch (or imagine) the graph of |x-2|. You should know it has something to do with \pm (x-2) and it is precisely the fact that for x<2 we have that portion of the graph equal to 2-x
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    (Original post by RDKGames)
    By definition of |x| we have |x-2| = 2-x for x < 2. Clearly, when you're talking about the interval 1<x<2 this is just a subinterval of x<2.

    Otherwise, you can just sketch (or imagine) the graph of |x-2|. You should know it has something to do with \pm (x-2) and it is precisely the fact that for x<2 we have that portion of the graph equal to 2-x
    thanks but i was asking about the interval
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    (Original post by man111111)
    thanks but i was asking about the interval
    I meant to write 0<x<1. The post applies.
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    (Original post by man111111)
    why do you multiply x-2 with -1
    Look. The only thing you really need to know about modulus is that (*)

    |f(x)| = \left\{ 	\begin{array}{ll} f(x) & \mbox{if } f(x) \geq 0 \\ 		-f(x) & \mbox{if } f(x) &lt; 0 	\end{array} \right.

    So, if someone says |x-2| = 2-x, the reason is going to be because x-2 < 0 (and then using (*)).

    The fact that you keep asking "why has ... been multiplied by -1"? makes me think you are not understanding the fundamental definition (*).
 
 
 
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