Answer
The correct solution is $ x\lt -9$.
The second step is wrong, $>$ remains the same.
Work Step by Step
The given inequality is
$\Rightarrow -6\gt \frac{2}{3}x$
Multiply each side by $\frac{3}{2}$.
$\Rightarrow \frac{3}{2}\cdot (-6)\gt \frac{3}{2}\cdot \frac{2}{3}x$
Clear the parentheses.
$\Rightarrow -\frac{18}{2}\gt x$
Simplify.
$\Rightarrow -9\gt x$
Hence, the correct solution is $ x\lt -9$.
The second step is wrong, $>$ remains the same.
