If a number line has an open dot at -12 and shading to the left, which inequality is correct?

Correct answer: x < -12

A horizontal number line increases from left to right, so points to the left of -12 represent numbers smaller than -12. The shading therefore describes x values less than -12. The open dot is equally important: it means the boundary value -12 is excluded, so equality is not allowed. Combining the direction of shading with the type of endpoint gives x < -12, making option C correct. Option A has the correct left-side direction but uses ≤ and would require a closed dot at -12. Options B and D describe numbers to the right of -12, and D also includes the boundary. Thus neither the direction nor the endpoint in those options matches the stated diagram.