## Thinking Mathematically (6th Edition)

the solution set is $\left\{ 0 \right\}$.
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 $\left\{ 0 \right\}$.