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Math Help - ACT Math Help

  1. #1
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    ACT Math Help

    I'm studying for the ACT and I can't figure out how to do this problem. I feel like it should be easy, but I really need an explanation.

    (I can't make a less-than-or-equal-to sign on my keyboard, so when you see a * that's what it means.)
    When -3 * x * 4 and -1 * y * 2, what is the least possible value for x - y?

    F. -5
    G. -3
    H. -2
    J. 3
    K. 5

    I know that the answer is F. but I need an explanation why.
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  2. #2
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    May 2009
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    -3\leq x\leq 4 and -1\leq y \leq 2 we basically want x to be as small as possible and then we want y to be as large as possible since we are subtracting y from x,

    -3-2=-5 F

    this can be shown over the domain using calculus, but for the act, you certainly don't need calc
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  3. #3
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    Aug 2009
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    -1\leq y\leq 2 (given)
    -2\leq -y\leq 1 (multiply by -1)
    -2-3\leq x-y\leq 1+4 (add the other given inequality)
    -5\leq x-y\leq 5 (simplify)

    Hence -5 is the answer
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