To solve the inequality 4 - 2√(x-1) > 8, we can start by isolating the square root term.

First, subtract 4 from both sides of the inequality:
-2√(x-1) > 4

Next, divide both sides by -2. Since we are dividing by a negative number, the inequality sign will flip:
√(x-1) < -2

Now, square both sides of the inequality to eliminate the square root:
(x-1) < (-2)^2
x - 1 < 4
x < 4 + 1
x < 5

Therefore, the solution to the inequality 4 - 2√(x-1) > 8 is x < 5.