To solve the equation $|8 - 2x| = 16$, we need to remove the absolute value by considering the two possible cases:

Case 1: Positive expression

$8 - 2x = 16$ Solving for $x$: $8 - 2x = 16 \implies -2x = 16 - 8 \implies -2x = 8 \implies x = \frac{8}{-2} = -4$ This is a solution, but we need the positive value of $x$, so this one is not valid.

Case 2: Negative expression

$8 - 2x = -16$ Solving for $x$: $8 - 2x = -16 \implies -2x = -16 - 8 \implies -2x = -24 \implies x = \frac{-24}{-2} = 12$ This gives us $x = 12$, which is a positive value.

Final Answer:

The positive value of $x$ that satisfies the equation is $x = 12$.

Would you like more details or have any questions? Here are 5 related questions you can try:

1. Solve $|3x - 5| = 10$ for $x$.
2. Find $x$ such that $|2x + 7| = 13$.
3. Solve $|5 - x| = 9$ and identify the positive solution.
4. How do you solve $|x + 3| = 7$?
5. What is the solution to $|4x - 8| = 20$?

Tip: When solving absolute value equations, always remember to split them into two cases: one for the positive and one for the negative.