Question

Mark the correct alternative in each of the following:
If x$<$7, then
(a) $-$x$<$$-$7
(b) $-$x$\le -$7
(c) $-$x$>-$7
(d) $-$x$\ge -$7

Answer 1

$$\begin{gathered} x<7 \\ \mathrm{subtracting}x\mathrm{on}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ \Rightarrow x-x<7-x \\ \Rightarrow 0<7-x \\ \mathrm{subtracting}7\mathrm{on}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ \Rightarrow 0-7<7-x-7 \\ \Rightarrow -7<-x \\ \Rightarrow -x>-7 \end{gathered}$$

Hence, the correct option is (c).