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# How many integers $m \neq 0$ satisfy the inequality $\frac{1}{|m|}\geq \frac{1}{8}$?

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How many integers $m \neq 0$ satisfy the inequality $\frac{1}{|m|}\geq \frac{1}{8}$?

May 18, 2021

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Case 1: m>0. Then, m<=8 so there are 8 values.

Case 2: m<0. Then, there are also 8 values, the negatives of the values in Case 1.

So, there 16 values total.

May 19, 2021