Question

If $1\le |x|<4$, then $x$ belongs to

• A. $(-4,-1]\cup [1,4)$
• B. $(-4,4)$
• C. $[-1,1]$
• D. $(-\infty ,-4)\cup (4,\infty )$

Answer 1

The correct option is A $(-4,-1]\cup [1,4)$

$1\le |x|<4$
When
$1\le |x|$
$\Rightarrow (-\infty ,-1]\cup [1,\infty )\cdots \left(1\right)$
Also,
$|x|<4$
$\Rightarrow -4<x<4\cdots \left(2\right)$
From $\left(1\right)$ and $\left(2\right)$, we get
$\therefore x\in (-4,-1]\cup [1,4)$