Question

ellen drew a graph showing the solution to an inequality.

number line with open circle at -0.75, arrow to the left

which inequality does ellen’s graph show the solution to?

○ 3.25 < 2.5 + r
○ 3.25 > 2.5 + r
○ -3.25 < -2.5 + r
○ -3.25 > -2.5 + r

Explanation:

Step1: Analyze the graph

The graph has an open circle at \( r = -0.75 \) and the arrow points to the left, so the solution is \( r < -0.75 \).

Step2: Solve each inequality

• For \( 3.25 < 2.5 + r \): Subtract \( 2.5 \) from both sides: \( 3.25 - 2.5 < r \) → \( 0.75 < r \) (not matching).
• For \( 3.25 > 2.5 + r \): Subtract \( 2.5 \): \( 3.25 - 2.5 > r \) → \( 0.75 > r \) (not matching).
• For \( -3.25 < -2.5 + r \): Add \( 2.5 \): \( -3.25 + 2.5 < r \) → \( -0.75 < r \) (not matching).
• For \( -3.25 > -2.5 + r \): Add \( 2.5 \): \( -3.25 + 2.5 > r \) → \( -0.75 > r \) (matches \( r < -0.75 \)).

Answer:

D. \( -3.25 > -2.5 + r \)