Question

If $3\le |x|\le 5$, then which of the following can be true?

• A. $x\in [-3,3]$
• B. $x\in (-3,3)$
• C. None of these
• D. $x\in [-5,-3]\cup [3,5]$

Answer 1

The correct option is D $x\in [-5,-3]\cup [3,5]$

Given that $3\le |x|\le 5$

From the properties of the Modulus Function,
If $a\le |x|\le b$, where $a,b>0$ then
$-b\le x\le -a$ or $a\le x\le b$
$\Rightarrow x\in [-b,-a]\cup [a,b]$

Here we have $3\le |x|\le 5\Rightarrow x\in [-5,-3]\cup [3,5]$