Solve the inequality 6x+9>57. Which of the following graphs shows the solution?(1 point)

Question

Responses

A. A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.

B .A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.

C .A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 11. A rightward arrow is marked on the number line that originates at the open point and goes beyond 18.

D .A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
Image with alt text: A number line is shown ranging from negative 2 to 18 with numbers listed in unit increments. An open point is plotted on the number line at 8. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 2.
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Answer 1

To solve the inequality \( 6x + 9 > 57 \), follow these steps:

1. Subtract 9 from both sides: \[ 6x > 57 - 9 \] \[ 6x > 48 \]

2. Divide both sides by 6: \[ x > \frac{48}{6} \] \[ x > 8 \]

The solution to the inequality is \( x > 8 \).

Now, let's analyze the options provided based on this solution:

1. Option A: Open point at 11 with a leftward arrow – This represents \( x < 11 \), which is not the correct solution.

2. Option B: Open point at 8 with a rightward arrow – This represents \( x \geq 8 \), which is also not correct as it should be strictly greater than 8.

3. Option C: Open point at 11 with a rightward arrow – This represents \( x > 11 \), which is too restrictive compared to the solution.

4. Option D: Open point at 8 with a leftward arrow – This represents \( x < 8 \), which is also not correct.

Thus, none of the provided options accurately represent the solution \( x > 8 \). The correct graph would need to have an open point at 8 and a rightward arrow extending beyond 8. However, based on the closest options, Option B can be interpreted as correct if it includes the idea of numbers greater than 8 (despite it technically including 8).

If you need to choose among provided responses based strictly on the indication of \( x > 8 \), you would likely go with Option B since it represents values greater than or equal to 8 but acknowledge it does not capture the strict inequality \( x > 8 \).