The region satisfying the inequality \(3x + 7y \gt 21\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → The half plane that neither contains the origin nor the points of the line
The line \(3x + 7y = 21\) divides the plane into two half planes. Testing the origin (0, 0):
\( 3(0) + 7(0) = 0 \)
\( 0 \gt 21 \) is false
So the origin does not satisfy the inequality, and the region is the half plane on the side away from the origin.
Since the inequality is strict (\(\gt\), not \(\ge\)), the points on the line \(3x + 7y = 21\) are not included either.