If $\left|\frac{12}{x}+3\right|=2$, find the product of all possible values of $x$. Express your answer as an improper fraction.

Guest May 11, 2020

#1**+2 **

Hi Guest!

If \(\left|\frac{12}{x}+3\right|=2\) find the product of all possible values of \(x\). Express your answer as an improper fraction.

Ok, so let's start off by solving the equation. \(|\frac{12}{x}+3|=2\)

So, we know that \(\frac{12}{x}+3=2\) **OR \(\frac{12}{x}+3=-2\)**

The first equation:

\(\frac{12}{x}+3=2\)

\(\frac{12}{x}=-1\)

\(12=-1x\)

\(x=-12\)

The second equation:

\(\frac{12}{x}+3=-2\)

\(\frac{12}{x}=-5\)

\(12=-5x\)

\(x=-\frac{12}{5}\)

They are asking for the product of the possible values, so we **multiply -12 and -12/5.**

\(-12 \cdot -\frac{12}{5}=\boxed{\frac{144}{5}}\)

PS. please use LaTex next time in your question!

I hope this helped you, guest!

:)

lokiisnotdead May 11, 2020