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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 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 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 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 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 can 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 graph options provided:

  • The correct representation for \(x > 8\) would be an open point at 8 (indicating that 8 is not included in the solution) with a rightward arrow extending past 8, showing all numbers greater than 8.

Based on the options described:

  • The second option shows an open point at 8 with a rightward arrow going beyond 18, which correctly represents the solution to the inequality \(x > 8\).

Therefore, the appropriate graph that shows the solution is the second option.