Answer
the solution set is \[\left\{ 0 \right\}\].
Work Step by Step
The equation is \[\frac{x}{2}-\frac{x}{4}+4=x+4\].
Subtract \[4\]from both sides of the equal sign.
\[\begin{align}
& \frac{x}{2}-\frac{x}{4}+4-4=x+4-4 \\
& \frac{x}{2}-\frac{x}{4}=x \\
& \frac{2x}{4}-\frac{x}{4}=x \\
& \frac{x}{4}=x \\
\end{align}\]
Multiply by 4 both sides of the equal sign.
\[x=4x\]
Subtract \[x\]from both sides of the equal sign.
\[\begin{align}
& x-x=4x-x \\
& 0=3x \\
& 0=x \\
\end{align}\]
Check the proposed solution. Substitute 0 for x in the original equation \[\frac{x}{2}-\frac{x}{4}+4=x+4\]
\[\begin{align}
& \frac{0}{2}-\frac{0}{4}+4=0+4 \\
& 4=4 \\
\end{align}\]
This true statement \[4=4\] verifies that the solution set is \[\left\{ 0 \right\}\].
Thus, the solution set is \[\left\{ 0 \right\}\].
