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Solve the inequality 6x+9>57

. Which of the following graphs shows the solution?(1 point)
Responses

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.

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.

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.

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.

1 answer

To solve the inequality \( 6x + 9 > 57 \), we start by isolating \( x \):

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

  2. Next, divide both sides by \( 6 \): \[ x > 8 \]

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

On a number line, this is represented by an open point at \( 8 \) (indicating that \( 8 \) is not included in the solution) and a rightward arrow from \( 8 \) (indicating that \( x \) can take on any value greater than \( 8 \)).

Looking at the options:

  • The correct option is the one that has an open point at \( 8 \) and a rightward arrow extending beyond \( 18 \).

Based on the description you provided, this matches the second option: "A number line is shown ranging from negative 2 to 18 with an open point 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."

So the answer is the second graph.