Answer
$x<2$
Work Step by Step
Create a table of values of $x$ and $y$ where $x$ is positive and $y$ is formulated by $y=\frac{5}{x-2}$.
$\begin{matrix}
\hline
x&y\\
\hline
0&-2.5\\
0.5&-3.333\\
1&-5.0\\
1.5&-10.0\\
2&\text{Error}\\
2.5&10.0\\
3&5.0\\
\hline
\end{matrix}$
In the table, we get two conditions: $y<0$ for $x<2$ and $y>0$ for $x>2$.
Equivalently, $\frac{5}{x-2}<0$ if $x<2$ and $\frac{5}{x-2}>0$ if $x>2$.
Thus, the solution to the inequality is $x<2$.
