Solve: $8-2|x-8|>4$ Give your answer as an interval.

Step 1 ：The inequality \(8-2|x-8|>4\) means that the distance between \(x\) and \(8\) on the number line, multiplied by \(-2\) and added to \(8\), is greater than \(4\). This can be solved by first isolating the absolute value term.

Step 2 ：Subtract \(8\) from both sides of the inequality to get \(-2|x-8|>-4\)

Step 3 ：Then divide both sides by \(-2\) to get \(|x-8|<2\). Remember that when you divide by a negative number, the direction of the inequality sign changes.

Step 4 ：This inequality can be solved by setting up two inequalities: \(x-8<2\) and \(-(x-8)<2\)

Step 5 ：Solving these inequalities gives us the solutions \(x=10\) and \(x=6\). However, these are the endpoints of the interval of solutions.

Step 6 ：The solution to the original inequality \(8-2|x-8|>4\) is the interval \((6, 10)\)

Step 7 ：Final Answer: The solution to the inequality \(8-2|x-8|>4\) is \(\boxed{(6, 10)}\)