Answer
The solution set is \[\left\{ \frac{7}{2} \right\}\].
Work Step by Step
The equation is\[\frac{x-2}{5}=\frac{3}{10}\].
Apply the cross-product principle in the equation.
\[\begin{align}
& \frac{x-2}{5}=\frac{3}{10} \\
& 10\left( x-2 \right)=3\times 5 \\
& 10x-20=15 \\
\end{align}\]
Add20to both sides of the equal sign.
\[\begin{align}
& 10x-20+20=15+20 \\
& 10x=35 \\
\end{align}\]
Divided by \[10\], both sides of the equal sign.
\[\begin{align}
& \frac{10x}{10}=\frac{35}{10} \\
& x=\frac{7}{2} \\
\end{align}\]
Check the proposed solution. Substitute \[\frac{7}{2}\] for x in the original equation \[\frac{x-2}{5}=\frac{3}{10}\].
\[\begin{align}
& \frac{\frac{7}{2}-2}{5}=\frac{3}{10} \\
& \frac{\frac{7-4}{2}}{5}=\frac{3}{10} \\
& \frac{3}{2\times 5}=\frac{3}{10} \\
& \frac{3}{10}=\frac{3}{10} \\
\end{align}\]
This true statement \[\frac{3}{10}=\frac{3}{10}\] verifies that the solution set is \[\left\{ \frac{7}{2} \right\}\].
Thus, the solution set is \[\left\{ \frac{7}{2} \right\}\].
