1. **State the problem:** Solve the equation $$\frac{-11 + x}{-7} = -15$$ for $x$. 2. **Understand the formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. Since $x$ is in a fraction, we can start by eliminating the denominator by multiplying both sides by $-7$. 3. **Multiply both sides by $-7$:** $$\cancel{-7} \times \frac{-11 + x}{\cancel{-7}} = -15 \times -7$$ This simplifies to: $$-11 + x = 105$$ 4. **Isolate $x$ by adding 11 to both sides:** $$-11 + x + 11 = 105 + 11$$ $$x = 116$$ 5. **Final answer:** $$x = 116$$ This means the value of $x$ that satisfies the equation is 116.