Solve the inequality. \[ 2 x-4 x \leq x+2 \] The solution set is $\{x$ (Use integers or fractions for any numbers in the expression.)

Step 1 ：The inequality is in the form of a linear inequality. To solve it, we need to simplify the inequality and isolate the variable x on one side of the inequality.

Step 2 ：Simplify the inequality to get \(-2x \leq x + 2\).

Step 3 ：Solving for x gives the solution \(x = -\frac{2}{3}\).

Step 4 ：Check if this solution satisfies the original inequality. Substituting \(x = -\frac{2}{3}\) into the original inequality, we find that it holds true.

Step 5 ：Therefore, the solution set is \(\{x | x \leq -\frac{2}{3}\}\).

Step 6 ：Final Answer: The solution set is \(\boxed{\{x | x \leq -\frac{2}{3}\}}\).