Which one of the following is correct ? If `4 ltx^(2) le9` , then

Options

A. ` 2 lt x lt3 only`
B. `-3 lt x lt -2 only`
C. ` 2 lt x lt 3, -3 lt x lt - 2 `
D. None of these

Answer

C

Explanation

In the given inequality
` :' 4 lt x^(2) lt9`
We consider
` x^(2) gt 4 and x^(2) lt 9`
We first consider,
` x^(2) gt 4 rArr x^(2) - 4 gt0`
`rArr x gt -2 and x lt 2 `
Next , `X^(2) lt 9`
` x^(2) - 9 lt 0 " "rArr-3 lt x lt 3`
Combining both we get `-3 lt x lt -2,2 lt x lt3`
We represent this on number line

`rArr -3 lt x lt -2 and 2 ltx lt 3`