Answer
The second step is wrong. The correct solution is $-\frac{1}{2}\gt x \gt -3$.
The correct graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 4\lt -2x+3 \lt 9$
Subtract $3$ from each expression.
$\Rightarrow 4-3\lt -2x+3-3 \lt 9-3$
Simplify.
$\Rightarrow 1\lt -2x \lt 6$
Divide each side by $-2$. Reverse the inequality symbol.
$\Rightarrow \frac{1}{-2}\gt \frac{-2x}{-2} \gt \frac{6}{-2}$
Simplify.
$\Rightarrow -\frac{1}{2}\gt x \gt -3$
Hence, the second step is wrong. The correct solution is $-\frac{1}{2}\gt x \gt -3$.
