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

May 11, 2020

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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.

$$-12 \cdot -\frac{12}{5}=\boxed{\frac{144}{5}}$$

I hope this helped you, guest!

:)

May 11, 2020
edited by lokiisnotdead  May 11, 2020