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Inequalities: Simultaneous Inequalities

If $$-32 ≤ x ≤ 14$$ and $$-17 ≤ y ≤ 11$$, which of the following inequalities gives all possible values of $$x-y$$?


[[snippet]] Subtract maximum $$y$$ (i.e., $$11$$) from minimum $$x$$ (i.e., $$-32$$) to get the minimum value of $$x-y$$. >$$-32 - 11 = -43$$ Likewise, subtract minimum $$y$$ (i.e., $$-17$$) from maximum $$x$$ (i.e., $$14$$) to get the maximum value of $$x-y$$. >$$14 - (-17) = 14 + 17 = 31$$ Hence, the minimum and maximum values of $$x-y$$ are $$-43$$ and $$31$$, respectively.








[[snippet]] This answer is the result of directly subtracting inequalities, which is not allowed. The only operation you allowed to do to combine inequalities is addition.
$$-31 \le x-y \le 43$$
$$-43 \le x-y \le 31$$
$$-21 \le x-y \le 31$$
$$-15 \le x-y \le 3$$
$$-49 \le x-y \le 25$$