Question:
Mark the correct alternative in each of the following:
If $x<7$, then
(a) $-x<-7$
(b) $-x \leq-7$
(c) $-x>-7$
(d) $-x \geq-7$
Solution:
$x<7$
subtracting $x$ on both sides, we get
$\Rightarrow x-x<7-x$
$\Rightarrow 0<7-x$
subtracting 7 on both sides, we get
$\Rightarrow 0-7<7-x-7$
$\Rightarrow-7<-x$
$\Rightarrow-x>-7$
Hence, the correct option is (c).