Question

The value(s) of $x$ satisfying the equation $||x-3|-4|=3$, is/are

• A. $-4$
• B. $4$
• C. $6$
• D. $10$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $-4$
B $4$
D $10$

$||x-3|-4|=3$

$\text{Case}1:|x-3|-4=3$
$\Rightarrow |x-3|=7$
$\Rightarrow x-3=\pm 7$
$\Rightarrow x=10$ or $x=-4$
$\therefore x=-4,10\cdots \left(1\right)$

$\text{Case}2:|x-3|-4=-3$
$\Rightarrow |x-3|=1$
$\Rightarrow x-3=\pm 1$
$\Rightarrow x=2,4\cdots \left(2\right)$

Hence, from $\left(1\right)$ and $\left(2\right)$, $x=-4,2,4,10$