The solution region of the inequality 2x+4y ≤ 9 is:

The correct answer is Option (2) → closed half plane containing origin

The sign is ≤ (“less than or equal to”), so the points of the line 2x + 4y = 9 also satisfy the inequality. A half plane that includes its boundary line is a closed half plane; with a strict sign (< or >) it would be open.

Testing the origin:

    \(2(0) + 4(0) = 0 \le 9\), true

So the solution region is the closed half plane on the side of the line that contains the origin.