Question

If $||x-3|+4|\ge 2$, then $x$ belongs to

• A. $\varphi$
• B. $[-5,\infty )$
• C. $(-\infty ,-5]\cup [1,\infty )$
• D. $R$

Answer 1

The correct option is D $R$

$||x-3|+4|\ge 2$
$\Rightarrow |x-3|+4\le -2$ or $|x-3|+4\ge 2$
$\Rightarrow |x-3|\le -6$ (not possible)
or $|x-3|\ge -2$ (always)
For any real value of $x$, $|x-3|\ge 0$
So, $x\in R$