Answer
$r\lt2$ or $r\geq 7$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 2r+3\lt 7$ or $-r+9 \leq 2$
Solve the first inequality.
$\Rightarrow 2r+3\lt 7$
Subtract $3$ from each side.
$\Rightarrow 2r+3-3\lt 7-3$
Simplify.
$\Rightarrow 2r\lt 4$
Divide each side by $2$.
$\Rightarrow \frac{2r}{2}\lt \frac{4}{2}$
Simplify.
$\Rightarrow r\lt 2$
Solve the second inequality.
$\Rightarrow -r+9 \leq 2$
Add $r-2$ to each side.
$\Rightarrow -r+9+r-2 \leq 2+r-2$
Simplify.
$\Rightarrow 7 \leq r$
Hence, the solution is $r\lt2$ or $r\geq 7$.
