Solution assignment 10 Linear equations

For which value(s) of $p$ does the following equation have exactly one solution $x$ :

$p(x-1)+2=x-2p-1$

We can write this equation as:

$(p-1)x=-p-3$

$(p-1)x=-(p+3)$

This equation has only one solution $x$ if:

$p\neq1$

This means in this case that the solution is:

$x=-\displaystyle\frac{p+3}{p-1}$