Answer
always
Work Step by Step
For the equation $| x - p | = q$, the number of solutions depends on the value $q$ on the right hand side of the equation:
- if $q>0$, then $2$ solutions
- if $q = 0$, then only one solution
- if $q<0$, then no solution.
Here, the value on the right hand side is $q=4$ which is greater than $0$. Hence, the equation will $\textbf{always}$ have $2$ solutions irrespective of the value of $p$.
