#### Answer

The solution set is \[\varnothing \](the empty set).

#### Work Step by Step

The equation is\[\frac{x}{4}+3=\frac{x}{4}\].
Subtract \[\frac{x}{4}\] from both sides of the equal sign.
\[\begin{align}
& \frac{x}{4}+3-\frac{x}{4}=\frac{x}{4}-\frac{x}{4} \\
& 3=0
\end{align}\]
Therefore, the equation \[\frac{x}{4}+3=\frac{x}{4}\] is equivalent to the statement \[3=0\].
Which is false for every value of \[x\].
Thus, the equation has no solution. The solution set is \[\varnothing \](the empty set).