Solve the inequality. \[ \begin{array}{c} \frac{-4(x-2)}{2} \leq-x \\ x \geq[?] \end{array} \]

Step 1 ：Solve the inequality \(\frac{-4(x-2)}{2} \leq -x\).

Step 2 ：Simplify the left side of the inequality to get \(4 - 2x\).

Step 3 ：Add \(x\) to both sides of the inequality to get \(4 \leq x\).

Step 4 ：Rearrange the inequality to get \(x \geq 4\).

Step 5 ：The solution to the inequality is \(\boxed{x \geq 4}\). This means that any value of \(x\) that is greater than or equal to 4 will satisfy the inequality.