Question

Solve the equation. $$|2 x-4|-8=10$$

Short answer

The solutions to the equation are \(x = 11\) and \(x = -7\).

Step-by-step solution

Isolate the Absolute Value

To start with, isolate the absolute value on one side by adding 8 to both sides of the equation: \( |2x - 4| = 18 \)

Separate into Two Equations

Next, separate the equation into two separate ones. One where \(2x - 4 = 18\) and another where \(2x - 4 = -18\)

Solve Each Equation

Now, solve each equation separately. For the first equation, add 4 to both sides to get \(2x = 22\), then divide by 2 to find \(x = 11\). For the second equation, add 4 to both sides to get \(2x = -14\), and divide by 2 to find \(x = -7\)