Which linear inequality matches a graph with a boundary at x = 5 and shading to the left?

Which linear inequality matches a graph with a boundary at x = 5 and shading to the left?

• A. x < 5
• B. x > 5
• C. x ≤ 5
• D. x ≥ 5

Answer: (A)

A vertical boundary at x = 5 divides the plane into left and right regions. Shading to the left means every point in the shaded area has an x-coordinate less than 5. Since the boundary line itself isn’t included in the shaded region, the inequality uses a strict “less than.” So the matching inequality is x < 5. If the line were solid and included, it would be x ≤ 5.

A vertical boundary at x = 5 divides the plane into left and right regions. Shading to the left means every point in the shaded area has an x-coordinate less than 5. Since the boundary line itself isn’t included in the shaded region, the inequality uses a strict “less than.” So the matching inequality is x < 5. If the line were solid and included, it would be x ≤ 5.