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

Jan 21, 2015

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

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 $\setminus \frac{| m |}{8} = 1$, 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 $| \setminus \frac{m}{8} | = 1$ if and only if $m = \setminus \pm 8$