Answer
The provided statement is true.
Work Step by Step
Consider the provided inequality,
$\frac{x-2}{x+3}<2$.
Multiply both sides by ${{\left( x+3 \right)}^{2}}$ such that, $x\ne -3$
${{\left( x+3 \right)}^{2}}\frac{x-2}{x+3}<2{{\left( x+3 \right)}^{2}}$
Solve further to get,
$\begin{align}
& \left( x+3 \right)\left( x-2 \right)<2{{\left( x+3 \right)}^{2}} \\
& \left( x-2 \right)<2\left( x+3 \right) \\
& x-2<2x+6 \\
& x>8
\end{align}$
Hence, the provided statement is true.
