If $\left|\frac{12}{x}+3\right|=2$, find the product of all possible values of $x$. Express your answer as an improper fraction.
+738 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!
:)
