help algebra 1 stuff

Note that we have two equations

2x  -  4  =   8                   and                        -(2x - 4)  =  8

2x - 4   =  8                                                    -2x +  4   = 8

add 4 to both sides                                      subtract 4 from each side

2x   =    12                                                      -2x   =    4

divide both sides by 2                                  divide both sides by -2

x   =   6                                                               x  =   -2  

And those are the two solutions

If |2x – 4| = 8 then x = _____ and _____

Formula:

$\begin{array}{|rcll|} \hline x^2=|x^2| = |x|^2 \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline |2x – 4| &=& 8 \\ |2x – 4|^2 &=& 8^2 \quad & |2x – 4|^2 = (2x – 4)^2 \\ (2x – 4)^2 &=& 8^2 \\ [2\cdot(x – 2)]^2 &=& 8^2 \\ 2^2\cdot(x – 2)^2 &=& 8^2 \\ 4\cdot (x – 2)^2 &=& 64 \quad & | \quad : 4 \\ (x – 2)^2 &=& 16 \quad & | \quad \text{square root both sides } \\ x – 2 &=& \pm\sqrt{16} \\ x – 2 &=& \pm 4 \quad & | \quad +2 \\ x &=& 2\pm 4 \\\\ x_1 &=& 2+4 \\ x_1 &=& 6 \\\\ x_2 &=& 2-4 \\ x_2 &=& -2 \\ \hline \end{array}$

x = -2 and  6