Answer
Not true because 1's reciprocal is 1, and they are both integers.
Work Step by Step
The reciprocal of any integer $x$ is $\frac{1}{x}$, so usually $\frac{1}{x}$ is not an integer. But, if $x=1$, then $\frac{1}{1}$ would be an integer. This also works for -1.
