To solve the inequality \( 5x - 15 > -65 \), we first isolate \( x \) by adding 15 to both sides:
\[ 5x > -65 + 15 \]
\[ 5x > -50 \]
Next, we divide both sides by 5:
\[ x > -10 \]
Now, we interpret this solution. The inequality \( x > -10 \) means that \( x \) can be any number greater than \(-10\).
In terms of a number line representation:
- We place an open circle at \(-10\) indicating that \(-10\) is not included in the solution.
- We draw a bold line extending to the right from \(-10\) to indicate all numbers greater than \(-10\).
Therefore, the correct representation of the solution on a number line is:
C. The number line shows numbers from -12 to -8. There is an open circle at -10, a bold line from -10 heading rightwards.