## Thinking Mathematically (6th Edition)

The solution set is$\left\{ -\frac{5}{2} \right\}$.
The equation is$\frac{x+4}{8}=\frac{3}{16}$. Apply the cross-product principle in the equation. \begin{align} & \frac{x+4}{8}=\frac{3}{16} \\ & 16\left( x+4 \right)=3\times 8 \\ & 16x+64=18 \\ \end{align} Subtract $64$from both sides of the equal sign. \begin{align} & 16x+64-64=18-64 \\ & 16x=-40 \\ \end{align} Divided by $16$, both sides of the equal sign. \begin{align} & \frac{16x}{16}=\frac{-40}{16} \\ & x=-\frac{5}{2} \\ \end{align} Check the proposed solution. Substitute $\frac{-5}{2}$ for x in the original equation$\frac{x+4}{8}=\frac{3}{16}$. \begin{align} & \frac{\frac{-5}{2}+4}{8}=\frac{3}{16} \\ & \frac{\frac{-5+8}{2}}{8}=\frac{3}{16} \\ & \frac{3}{2\times 8}=\frac{3}{16} \\ & \frac{3}{16}=\frac{3}{16} \\ \end{align} This true statement $\frac{3}{16}=\frac{3}{16}$ verifies that the solution set is$\left\{ -\frac{5}{2} \right\}$. Thus, the solution set is$\left\{ -\frac{5}{2} \right\}$.