Which value does not satisfy the inequality 5 − x ≥ 2?

Correct answer: x = 4

The governing concept is solving a linear inequality while preserving the correct order relation. Starting with 5 − x ≥ 2, subtract 5 from both sides to obtain −x ≥ −3. Multiplying or dividing an inequality by −1 reverses its sign, so x ≤ 3. Therefore every value less than or equal to 3 satisfies the inequality, while values greater than 3 do not. Testing the options confirms this: x = 3 gives 2 ≥ 2, x = 2 gives 3 ≥ 2, and x = 1 gives 4 ≥ 2. For x = 4, the left side is 1, and 1 ≥ 2 is false. Hence option A is the only value that does not satisfy the inequality. The other options are distractors because they lie within the solution set.