Answer
The solution set is \[\left\{ 0 \right\}\].
Work Step by Step
The equation is\[\frac{x}{3}=\frac{x}{2}\].
Apply the cross-product principle in the equation.
\[\begin{align}
& 2\times x=3\times x \\
& 2x=3x
\end{align}\]
Subtract \[2x\] from both sides of the equal sign.
\[\begin{align}
& 2x-2x=3x-2x \\
& 0=x \\
& x=0 \\
\end{align}\]
Check the proposed solution. Substitute \[0\] for x in the original equation \[\frac{x}{3}=\frac{x}{2}\].
\[\begin{align}
& \frac{0}{3}=\frac{0}{2} \\
& 0=0 \\
\end{align}\]
This true statement \[0=0\] verifies that the solution set is \[\left\{ 0 \right\}\].
Thus, the solution set is \[\left\{ 0 \right\}\].
