Mark the correct alternative in each of the following:
Question:

Mark the correct alternative in each of the following:

If $-3 x+17<-13$, then

(a) $x \in(10, \infty)$

(b) $x \in[10, \infty)$

(c) $x \in(-\infty, 10]$

(d) $x \in[-10,10)$

Solution:

$-3 x+17<-13$

Subtracting 17 on both sides, we get

$\Rightarrow-3 x+17-17<-13-17$

$\Rightarrow-3 x<-30$

Dividing $-3$ on both sides, we get

$\Rightarrow \frac{-3 x}{-3}>\frac{-30}{-3}$

$\Rightarrow x>10$

$\Rightarrow x \in(10, \infty)$

Hence, the correct option is (a).