Answer
The provided statement is false and the correct statement is “The inequality $\frac{x-2}{x+3}<2$ can be solved by multiplying both sides by $\left( x+3 \right)$ with $x\ne -3$ , resulting in the equivalent inequality $\left( x-2 \right)<2\left( x+3 \right)$.”
Work Step by Step
Consider the provided rational inequality,
$\frac{x-2}{x+3}<2$
If $x=-3$ , the above inequality cannot be divided by $\left( x+3 \right)$ as then the rational function will become undefined. Therefore, the provided inequality cannot be solved.
Hence, the provided statement is false.
The provided statement is false and the correct statement is “The inequality $\frac{x-2}{x+3}<2$ can be solved by multiplying both sides by $\left( x+3 \right)$ with $x\ne -3$ , resulting in the equivalent inequality $\left( x-2 \right)<2\left( x+3 \right)$.”
