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

Guest Apr 20, 2017
 #1
avatar+91135 
+1

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

 

 

 

cool cool cool                              

CPhill  Apr 20, 2017
 #2
avatar+20151 
+1

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

 

laugh

heureka  Apr 20, 2017
edited by heureka  Apr 20, 2017

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