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Math Help - Is my reasoning correct?

  1. #1
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    Is my reasoning correct?

    The question states:
    The length of two sides of a trangle are (x-2) and (x+2), where x>2. Which of the following ragnes includes all and only the possible values of the thrid side Y?
    A)0<y<x
    B)0<y<2x
    C)2<Y<x
    D)4<Y<x
    E)4<Y<2x

    I got the answer choice E. Apparently, though, the answer resulted to be B. What i dont get is, the question says "Which of the following ragnes includes all and only the possible values of the thrid side Y?" However, in the ranges between 0 and 2x, there are values that will be incorrect. Considering x=5, B will not satisfy it. If my reasoning is wrong, please teach me the correct way to look at the problem. Thank you guys
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  2. #2
    A riddle wrapped in an enigma
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    The possible values for the third side of a triangel given the other two sides is represented by this:

    (difference\; \; of \; \;other \; \;2 \; \;sides) < y < (sum \; \; of \; \; other \; \; two \; \; sides)

    Thus,

    (x+2)-(x-2)<y<(x-2)+(x+2)

    x+2-x+2<y<x-2+x+2

    4<y<2x
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