+128408 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
+26367 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
