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# Absolute value

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If |12/x+3|= 2, find the product of all possible values of x. Express your answer as an improper fraction.

the lines are absolute value

Aug 17, 2017

#1
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$$|\frac{12}{x}+3|=2$$

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

$$\frac{12}{x}+3-3=2-3$$     $$-\frac{12}{x}-3=2$$

$$\frac{12}{x}+0=2-3$$             $$-\frac{12}{x}-3+3=2+3$$

$$\frac{12}{x}=2-3$$                    $$-\frac{12}{x}+0=2+3$$

$$\frac{12}{x}=-1$$                        $$-\frac{12}{x}=2+3$$

$$\frac{12}{x}\times x=-1\times x$$        $$-\frac{12}{x}=5$$

$$12=-1\times x$$                 $$-\frac{12}{x}\times x=5\times x$$

$$12=-x$$                        $$-12=5\times x$$

$$\frac{12}{-1}=\frac{-x}{-1}$$                        $$\frac{-12}{5}=\frac{5x}{5}$$

$$-12=\frac{-x}{-1}$$                      $$-\frac{12}{5}=\frac{5x}{5}$$

$$-12=x$$                          $$-\frac{12}{5}=x$$

$$x=-12$$                          $$x=-\frac{12}{5}$$

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Aug 17, 2017
#2
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And their product is $${144\over5}$$

Mathhemathh  Aug 17, 2017