# How do you solve compound inequalities -2x + 1 > 3 and -2x + 1 < 9?

Using the shorthand notation $3 < - 2 x + 1 < 9$, first subtract 1 from all parts to give: $2 < - 2 x < 8$.
$- 1 > x > - 4$, i.e. $- 4 < x < - 1$.