Question

which graph shows the solution set of $-2x > 4$?

Explanation:

Step1: Solve the inequality \(-2x > 4\)

Divide both sides by \(-2\). Remember that when dividing an inequality by a negative number, the direction of the inequality sign flips. So we have \(x < \frac{4}{-2}\), which simplifies to \(x < -2\).

Step2: Analyze the number line graphs

• For a solution of \(x < -2\), the graph should have an open circle at \(-2\) (since \(x\) is not equal to \(-2\)) and the arrow should point to the left (towards negative infinity, where values are less than \(-2\)).
• Option A: Closed circle at \(-2\) (incorrect, since \(x

eq -2\)) and arrow left.

• Option B: Closed circle at \(-2\) (incorrect) and arrow left.
• Option C: Open circle at \(-2\) and arrow left (matches \(x < -2\)).
• Option D: Closed circle at \(-2\) (incorrect) and arrow left.

Answer:

C. The graph with an open circle at -2 and an arrow pointing to the left (towards values less than -2)