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

Answer: (B)

closed half plane containing origin

Answer 2

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.