find the values of x that satisfy the absolute inequality | 5 - X | ≤ 2

To solve the absolute inequality |5 - x| \leq 2, we need to consider two cases, one for when the expression inside the absolute value is positive and one for when it is negative.

Case 1: When 5 - x \geq 0 (i.e., 5 \geq x)
In this case, the absolute value expression |5 - x| simplifies to 5 - x, so the inequality becomes:
5 - x \leq 2

Solving for x:
5 - x \leq 2
-x \leq -3
x \geq 3

Case 2: When 5 - x < 0 (i.e., 5 < x)
In this case, the absolute value expression |5 - x| simplifies to - (5 - x) or -(5 - x), so the inequality becomes:
-(5 - x) \leq 2

Solving for x:
-(5 - x) \leq 2
-5 + x \leq 2
x \leq 7

Therefore, the values of x that satisfy the absolute inequality |5 - x| \leq 2 are x \geq 3 and x \leq 7.

\boxed{3 \leq x \leq 7}