Question

Mark the correct alternative in each of the following:
If − 3x$+$17$<-$13, then
(a) x$\in$(10, $\infty$)
(b) x$\in$[10, $\infty$)
(c) x$\in$($-\infty$, 10]
(d) x$\in$[$-$10, 10)

Answer 1

$$\begin{gathered} -3x+17<-13 \\ \mathrm{Subtracting}17\mathrm{on}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ \Rightarrow -3x+17-17<-13-17 \\ \Rightarrow -3x<-30 \\ \mathrm{Dividing}-3\mathrm{on}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ \Rightarrow \frac{-3x}{-3}>\frac{-30}{-3} \\ \Rightarrow x>10 \\ \Rightarrow x\in \left(10,\infty \right) \end{gathered}$$

Hence, the correct option is (a).