Question

Find the number of solutions of the equation ||$|x-1|-1|-1|=\frac{1}{2}$.

Answer 1

Answer: 6

||$|x-1|-1|-1|=\frac{1}{2}$
$\Rightarrow ||x-1|-1|=\frac{1}{2},\frac{3}{2}$
$\Rightarrow |x-1|=\frac{1}{2},\frac{3}{2},\frac{5}{2}$
$\Rightarrow x=\frac{1}{2},\frac{3}{2},\frac{-1}{2},\frac{5}{2},\frac{-3}{2},\frac{7}{2}$
$\Rightarrow$ Number of solutions are six.