## Thinking Mathematically (6th Edition)

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