Final answer:
The false statement about the graph of the inequality 2x + y ≤ 1 is option A, which claims that the point (2, 2) is located inside the shaded region. This is incorrect as substituting these values into the inequality shows that it does not satisfy the condition.
Step-by-step explanation:
To determine which statement is not true about the graph of the inequality 2x + y ≤ 1, we can analyze each given option by looking at the properties of the line and the shaded region it represents.
Option A: States that the point (2, 2) is located inside the shaded region. To verify this, we substitute x=2 and y=2 into the inequality: 2(2) + 2 = 6, which is not less than or equal to 1, so this statement is false, making it our answer. However, let's examine the other options for completeness.
Option B: Indicates the boundary is graphed as a solid line, which is true for inequalities that include ≤ or ≥, as these imply that points on the line satisfy the inequality.
Option C: Suggests the boundary is graphed along y - 2x + 1. This is an incorrect representation of the boundary line for the inequality 2x + y ≤ 1, so it is not accurate, although the correct inequality should be graphed along the line y = -2x + 1.
Option D: Claims the origin is located inside the shaded region. By substituting x=0 and y=0 into the inequality, we see that 0 ≤ 1, which is true, so the origin is indeed inside the shaded region.
Since Option A is false for the given inequality, it is the answer to the student's question.