Question

How do you solve for m given `|\frac{m}{8}|=1`?

Answer 1

Considering that `|\frac{a}{b}|= \frac{|a|}{|b|}`, you get that `|\frac{m}{8}|=1` if and only if `\frac{|m|}{|8|}=1`.

Now, obviously `|8|=8`, since 8 is a positive number and the absolute value of a number is the number itself is the number is positive, and the opposite otherwise.

So, we can rewrite the equality as `\frac{|m|}{8}=1`, which yields `|m|=8`

This request has two solutions. In fact, if `m` is positive, then `|m|=m`, and so we have `m=8`.

Otherwise, if `m` is negative, we have that `|m|=-m`, and thus `m=-8` solves the equation.

We conclude that `|\frac{m}{8}|=1` if and only if `m=\pm 8`