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

Answer 1

To solve the inequality 6x + 9 > 57, we can start by subtracting 9 from both sides:

6x + 9 - 9 > 57 - 9
6x > 48

Next, we divide both sides by 6 to isolate the variable x:

(6x)/6 > 48/6
x > 8

Therefore, the solution to the inequality is x > 8.

Looking at the given graphs:

-The first graph shows an open point at 8 on the number line and a leftward arrow that extends beyond -2. This represents x > 8, which is the correct solution.

-The second graph shows an open point at 11 on the number line and a rightward arrow that extends beyond 18. This does not represent x > 8, so it is not the correct solution.

-The third graph shows an open point at 11 on the number line and a leftward arrow that extends beyond -2. This represents x ≤ 11, which is incorrect.

Therefore, the first graph shows the correct solution to the inequality 6x + 9 > 57.