Absolute value

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

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