Simplify \( \frac{-21+\sqrt{49}}{-7} \) without using a calculator.

To simplify \( \frac{-21+\sqrt{49}}{-7} \), we start by calculating \( \sqrt{49} \). We know that \( \sqrt{49} = 7 \). Now substitute this back into the expression: \[ \frac{-21 + 7}{-7} \] Next, simplify the numerator: \[ -21 + 7 = -14 \] Now we have: \[ \frac{-14}{-7} \] When we divide \(-14\) by \(-7\), we get: \[ \frac{-14}{-7} = 2 \] Thus, the simplified form of the expression is: \[ \boxed{2} \]