Answer
The solution set is\[\left\{ -\frac{5}{2} \right\}\].
Work Step by Step
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\[\left\{ -\frac{5}{2} \right\}\].
