Question

The solution region of the inequality \( 2x + 4y \leq 9 \) is:

• A. open half plane containing origin
• B. closed half plane containing origin
• C. open half plane not containing origin
• D. closed half plane not containing origin

Answer 1

The Correct Option is B

Rewrite the inequality as:

\[ 2x + 4y = 9 \quad \text{(boundary line)}. \]

Test the origin \((0, 0)\) in the inequality:

\[ 2(0) + 4(0) \leq 9 \quad \text{True.} \]

Thus, the solution includes the origin. Since the inequality is \(\leq\), the boundary line is included, and the solution is the closed half-plane containing the origin.