Answer
The solution set is \[\left\{ 0 \right\}\].
Work Step by Step
The equation is\[\frac{x}{4}=\frac{x}{3}\].
Apply the cross-product principle in the equation.
\[\begin{align}
& 3\times x=4\times x \\
& 3x=4x
\end{align}\]
Subtract \[3x\] from both sides of the equal sign.
\[\begin{align}
& 3x-3x=4x-3x \\
& 0=x \\
& x=0 \\
\end{align}\]
Check the proposed solution. Substitute \[0\] for x in the original equation\[\frac{x}{4}=\frac{x}{3}\].
\[\begin{align}
& \frac{0}{4}=\frac{0}{3} \\
& 0=0 \\
\end{align}\]
This true statement \[0=0\] verifies that the solution set is \[\left\{ 0 \right\}\].
Thus, the solution set is \[\left\{ 0 \right\}\].
