To solve the inequality 6x + 9 > 57, we need to isolate x.
First, subtract 9 from both sides of the inequality:
6x + 9 - 9 > 57 - 9
6x > 48
Next, divide both sides of the inequality by 6:
6x/6 > 48/6
x > 8
The solution to the inequality is x > 8, which means x is greater than 8.
From the given responses:
Image A: The open point is plotted at 11 and a rightward arrow extends beyond 18. This does not show the solution, as it includes numbers greater than the solution.
Image B: The open point is plotted at 8 and a leftward arrow extends beyond negative 2. This does not show the solution, as it includes numbers less than the solution.
Image C: The open point is plotted at 11 and a leftward arrow extends beyond negative 2. This does not show the solution, as it includes numbers less than the solution.
Image D: The open point is plotted at 8 and a rightward arrow extends beyond 18. This correctly shows the solution, as it only includes numbers greater than 8.
Therefore, the correct response is the image with the rightward arrow on the number line starting at the open point plotted at 8.