Answer
sometimes
Work Step by Step
The value of $p$ can be greater than $0$, less than $0$ or equal to $0$.
The equation $|x - 4| = p$ will have $2$ solutions only when $p$ is greater than $0$.
It will have no solution when $p < 0$ and only one solution when $p=0$.
Hence, the statement is true only when $p>0$.
Therefore, for any real number $p$, the equation $|x-4|=p$ will $\textbf{sometimes}$ have $2$ solutions.
