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).
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