Solve $-12x 30$ when $x$ is a natural number.

Question

Solve $-12x > 30$ when $x$ is a natural number.

Accepted Answer

A. $\phi$ (empty set — no natural number satisfies it)

Divide by $-12$ (flip): $x < -30/12 = -5/2 = -2.5$.
Natural numbers are $\geq 1$, all positive. None can be less than $-2.5$. So the solution set is **empty**.
Over $\mathbb{Z}$, the solution would be $\{\ldots, -5, -4, -3\}$.

Answer

$\{1, 2\}$

Answer

$\{-3, -4, -5, \ldots\}$

Answer

$\{0\}$