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If $-3< x< -1$ , then
Option: 1
$-\frac{1}{3}<\frac{1}{x}<-1$

Option: 2
$9<x^{2}<1$

Option: 3
$0 \leqslant x^{2}<9$

Option: 4
$-1<\frac{1}{x}<-\frac{1}{3}.$

Answers (1)

best_answer

Sol: $-3<x<-1$

As $-3,-1<0$ , then we can square all 3 sides and change sign of inequality

$\begin{aligned} &(-3)^{2} >x^{2}>(-1)^{2} \\ \end{aligned}$

$\begin{aligned} \Rightarrow & 1<x^{2}<9 \end{aligned}$

Also $-3<x<-1$
For $\frac{1}{x}$ , we can take reciprocal of all 3 sides with change in sign of inequality

$\begin{aligned} &\text { (As }-3,-1<0 \text { ) } \\ \end{aligned}$

$\begin{aligned} &\frac{-1}{3}>\frac{1}{x}>-1 \end{aligned}$

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