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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
avatar+1876 
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                          \(|\frac{12}{x}+3|=2\)

 

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

 

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

 

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

 

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

 

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

 

\(\frac{12}{x}\times x=-1\times x\)        \(-\frac{12}{x}=5\)

 

\(12=-1\times x\)                 \(-\frac{12}{x}\times x=5\times x\)

 

\(12=-x\)                        \(-12=5\times x\)

 

\(\frac{12}{-1}=\frac{-x}{-1}\)                        \(\frac{-12}{5}=\frac{5x}{5}\)

 

\(-12=\frac{-x}{-1}\)                      \(-\frac{12}{5}=\frac{5x}{5}\)

 

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

 

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

.
 Aug 17, 2017
 #2
avatar+349 
+1

And their product is \({144\over5}\)

 

laugh

Mathhemathh  Aug 17, 2017

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