Inequalities: Simultaneous Inequalities

If $$7 \le x \le 34$$ and $$12 \le y \le 42$$, which of the following inequalities gives all possible values of $$x-y$$?

Incorrect. [[snippet]]

Incorrect. [[snippet]]

Incorrect. [[snippet]] Read the question carefully. This is the range of $$x+y$$.

Incorrect. [[snippet]] This is a trap option. Subtract the maximum $$y$$ from the minimum $$x$$ to get the minimum value of $$x-y$$. Likewise, subtract the minimum $$y$$ from the maximum $$x$$ to get the maximum value of $$x-y$$.

Correct. [[snippet]] Subtract the maximum $$y$$ (42) from the minimum $$x$$ (7) to get the minimum value of $$x-y$$: >$$\text{Minimum} = 7 - 42 = -35$$ Likewise, subtract minimum $$y$$ (12) from maximum $$x$$ (34) to get the maximum value of $$x-y$$: >$$\text{Maximum} = 34 - 12 = 22$$ Hence, the minimum and maximum values of $$x-y$$ are -35 and 22, respectively.

$$-35 \le x-y \le 22$$

$$-13 \le x-y \le 76$$

$$5 \le x-y \le 18$$

$$19 \le x-y \le 76$$

$$46 \le x-y \le 49$$