Question

determine whether the following statement is true or false. the graph of 5x - 6y > 3 includes the line 5x - 6y = 3. choose the correct answer below. a. the statement is false. the graph of an inequality never includes the line. b. the statement is true. the graph of an inequality with the > symbol includes the line, while the ≥ symbol does not include the line. c. the statement is false. the graph of an inequality with the > symbol does not include the line, while the ≥ symbol includes the line. d. the statement is true. the graph of an inequality always includes the line.

Explanation:

To determine the answer, we analyze the inequality symbols:

• For \( > \) or \( < \), the line is dashed (not included in the graph).
• For \( \geq \) or \( \leq \), the line is solid (included in the graph).

The inequality here is \( 5x - 6y > 3 \) (using \( > \)), so its graph does not include the line \( 5x - 6y = 3 \). Option C correctly states this: the statement is false, \( > \) does not include the line, while \( \geq \) does.

Answer:

C. The statement is false. The graph of an inequality with the > symbol does not include the line, while the ≥ symbol includes the line.