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  4. Find the number of solutions of the equation |||x-1|-1|-1|=(1/2).

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

Complex Numbers and Quadratic Equations

Solution:

||$|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.