Answer
the solution set is \[\left\{ 0 \right\}\].
Work Step by Step
The equation is \[\frac{x}{2}+\frac{2x}{3}+3=x+3\].
Subtract \[3\]from both sides of the equal sign.
\[\begin{align}
& \frac{x}{2}+\frac{2x}{3}+3-3=x+3-3 \\
& \frac{x}{2}+\frac{2x}{3}=x \\
& \frac{3x}{6}+\frac{4x}{6}=x \\
& \frac{7x}{6}=x \\
\end{align}\]
Multiply by \[6\] both sides of the equal sign.
\[7x=6x\]
Subtract \[6x\]from both sides of the equal sign.
\[\begin{align}
& 7x-6x=6x-6x \\
& x=0 \\
\end{align}\]
Check the proposed solution.Substitute 0 for x in the original equation \[\frac{x}{2}+\frac{2x}{3}+3=x+3\]
\[\begin{align}
& \frac{0}{2}+\frac{2\times 0}{3}+3=0+3 \\
& 0+0+3=3 \\
& 3=3 \\
\end{align}\]
This true statement \[3=3\] verifies that the solution set is \[\left\{ 0 \right\}\].
Thus, the solution set is \[\left\{ 0 \right\}\].
