# Math Help - ACT Math Help

1. ## 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.

2. $-3\leq x\leq 4$ 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

3. $-1\leq y\leq 2$ (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