Which inequality represents the half-plane to the right of the line x = 3?

Correct answer: x > 3

The line x = 3 is vertical, and every point on this line has x-coordinate exactly 3. Any point to its right has a larger x-coordinate, so the required half-plane is represented by x > 3. The strict inequality is used because the phrase “to the right” excludes the boundary line itself. If the boundary were included, the correct inequality would be x ≥ 3. Thus option C is correct. Option A, x < 3, describes the half-plane to the left of the line. Option B describes only the boundary, not a two-dimensional half-plane. Option D, y > 3, describes points above a horizontal line y = 3 and does not determine a region relative to the vertical line x = 3. Therefore only option C matches both the direction and the boundary.