Find the solution set of the in equation

$\frac{1}{x-2}<0$

We have to find values of $x$ for which $\frac{1}{x-2}$ is less than zero that is negative

Now for $\frac{1}{x-2}$ to be negative $x-2$ should be negative that is $x-2<0$

$\Rightarrow x-2<0$

$\Rightarrow x<2$

Hence $\mathrm{x}$ should be less than 2 for $\frac{1}{x-2}<0$

$x<2$ means $x$ can take values from $-\infty$ to 2 hence $x \in(-\infty, 2)$

Hence the solution set for $\frac{1}{x-2}<0$ is $(-\infty, 2)$