Solve the absolute equation \[ \begin{array}{l}|2 x-4|=10 \\ \text { a) } x=-3, x=7 \\ \text { b) } x=-7, x=3 \\ \text { c) } x=7 \\ \text { d) } x=-2, x=6\end{array} \]

To solve the absolute value equation \( |2x - 4| = 10 \), we need to set up two separate equations based on the definition of absolute value. 1. \( 2x - 4 = 10 \) 2. \( 2x - 4 = -10 \) For the first equation: \[ 2x - 4 = 10 \\ 2x = 10 + 4 \\ 2x = 14 \\ x = 7 \] For the second equation: \[ 2x - 4 = -10 \\ 2x = -10 + 4 \\ 2x = -6 \\ x = -3 \] Thus, the solutions to the equation \( |2x - 4| = 10 \) are \( x = 7 \) and \( x = -3 \). So the correct answer is: **a) \( x = -3, x = 7 \)**.