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If $4< x\leq 5$ then
Option: 1
$16< x^{2}< 25$

Option: 2
$16\leq x^{2}< 25$

Option: 3
$\frac{1}{5}\leq \frac{1}{x}< \frac{1}{4}$

Option: 4
$\frac{1}{4}< \frac{1}{x}\leq \frac{1}{5}$

Answers (1)

best_answer

Sol : $4< x\leq 5$

As both 4 and 5 are positive, so we can square all 3 sides.
$16<x^{2} \leqslant 25$
So (a) and (b) are wrong. $\cdot \quad 4<x \leqslant 5.$
As $4,5>0,$ we can take reciprocal a reverse sign of inequality
$\cdot \: \: \: \: \frac{1}{4}>x \geqslant \frac{1}{5} \Rightarrow \frac{1}{5} \leqslant x<\frac{1}{4}$
$\therefore$ (c) is correct

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