Solution assignment 08 Linear inequalities

For which value(s) of $p$ does the following inequality have no solution:

$p(x-2)+3<-(x+p)$

We can write this inequality as:

$px-2p+3<-x-p$

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

This inequality has no solution if:

$p+1=0$

thus if:

$p=-1$

For this value of $p$ the left-hand side is always equal to $0$ and the right-hand side is equal $-4$ .