The solution set of inequality $3x+5y < 4$ is

an open half plane containing the origin

The correct answer is Option (2) → an open half plane containing the origin

Given inequality: $3x + 5y < 4$

The corresponding line is $3x + 5y = 4$.

To determine which side of the line represents the solution, test the origin $(0,0)$.

Substitute $(0,0)$ into $3x + 5y < 4$:

$3(0) + 5(0) = 0 < 4$ → true.

Hence, the origin satisfies the inequality, and the region containing the origin is the required half-plane.

Since the inequality is strict (“<”), it represents an open half-plane.

Final answer: an open half-plane containing the origin.