<p>The set of all real numbers \(x\) satisfying \(x^2 - 5x + 6 \leq 0\) is:</p>
Step-by-Step Solution
Key Concept: Factorise: x^2-5x+6 = (x-2)(x-3). The product \leq 0 when x is between the roots (inclusive): [2, 3].
Notice that the best first move is to reveal the hidden structure in the expression. A clever move here is to rewrite the problem in the form where the standard theorem or identity applies cleanly. $x^2-5x+6 = (x-2)(x-3) \leq 0$. Sign chart: negative/zero between roots $x=2$ and $x=3$. Solution: $x \in [2,3]$. Now, we invoke the power of that idea, simplify patiently, and then check that the final answer really fits the original problem.
Correct Answer: A