Ask a New Question
Menu

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 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.
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.

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.

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. Divide both sides by \(6\): \[ x > 8 \]

This means the solution to the inequality is all real numbers greater than \(8\).

Now, let's interpret the graph options:

  • We need a number line with an open point at \(8\) and an arrow extending to the right (showing all values greater than \(8\)).

From the descriptions you've provided, the correct graph must represent the solution \(x > 8\). Therefore, the correct response is:

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.

This indicates that all numbers greater than \(8\) are included in the solution.