Answer
\[x=-15\].
Work Step by Step
Consider the equation\[\frac{x}{5}-2=\frac{x}{3}\].
The above equation can be written as:
\[\frac{x}{5}-\frac{2}{1}=\frac{x}{3}\]
The LCM is 15 so multiply by 15 both sides of the equation as follows:
\[\begin{align}
& \left( \frac{x}{5}-\frac{2}{1} \right)\times 15=\frac{x}{3}\times 15 \\
& \left( \frac{x}{5}\times 15 \right)-\left( \frac{2}{1}\times 15 \right)=\left( \frac{x}{3}\times 15 \right) \\
& 3x-30=5x
\end{align}\]
Subtract \[3x\]from both sides to get,
\[-30=2x\]
Divide both sides by 2 to get,
\[x=-15\]
Hence, the required solution is\[x=-15\].
