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Solve the inequality 6x+9>57

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

1.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.

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.

3.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.

4.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.

1 answer

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, we can check the options:

  1. The first graph shows an open point at 11 with a rightward arrow, indicating \( x \) can be greater than 11. This is not correct.

  2. The second graph shows an open point at 8 with a rightward arrow, indicating \( x \) can be greater than 8. This is correct.

  3. The third graph shows an open point at 11 with a leftward arrow, indicating \( x \) can be less than 11. This is not correct.

  4. The fourth graph shows an open point at 8 with a leftward arrow, indicating \( x \) can be less than 8. This is not correct.

The correct choice that represents the solution \( x > 8 \) is:

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.