Final Answer:
The graph represents the inequality x geq 3 The test point (3, 0) holds true for this inequality.
The correct answer is c) (x ≥3); (3, 0). The graph represents the inequality (x ≥3), and the test point (3, 0) holds true for this inequality.
Step-by-step explanation:
The given inequality is (x ≥ 3), indicating that \(x\) is greater than or equal to 3. The boundary line on the graph would be a solid line since the inequality includes equality. Points on or to the right of this line satisfy the inequality. The test point (3, 0) has an x-coordinate of 3. Substituting (x = 3) into the inequality, we get (3 ≥ 3), which is true. Therefore, the test point (3, 0) holds true for the inequality (x ≥ 3).
In the graph, if you shade the region to the right of the solid line representing (x = 3), you encompass all the values of (x) that make the inequality (x ≥ 3) true. This graphical representation aligns with the given inequality. The selection of test point (3, 0) was crucial for verification, and its confirmation ensures the accuracy of the chosen inequality. The solution is consistent with both the graphical representation and the algebraic evaluation, providing a comprehensive answer to the given question.
Therefore, the correct option is c) ( x geq 3 ); (3, 0)