Question

The number of solutions of $|\left[x\right]-2x|=4$, where $\left[x\right]$ is the greatest integer $\le x$, is:

• A. $2$
• B. $4$
• C. $1$
• D. infinite

Answer 1

The correct option is B $4$

Given, $\left|\right[x]-2x|=4$

$\Rightarrow \left[x\right]-2x=\pm 4$

$\Rightarrow -[${x}$+x]=\pm 4$

The possible values are $-4,4,3.5,-4.5$.

So, total $4$ values exist.