Question: Solve the equation, 11x + 4 = 10(x - 6) - 5, for the given variable.
1. **State the problem:** Solve the equation $$11x + 4 = 10(x - 6) - 5$$ for $$x$$.
2. **Apply the distributive property:** Expand the right side:
$$11x + 4 = 10x - 60 - 5$$
3. **Simplify the right side:**
$$11x + 4 = 10x - 65$$
4. **Isolate variable terms on one side:** Subtract $$10x$$ from both sides:
$$11x - \cancel{10x} + 4 = \cancel{10x} - 65$$
which simplifies to
$$x + 4 = -65$$
5. **Isolate $$x$$:** Subtract 4 from both sides:
$$x + \cancel{4} = -65 - \cancel{4}$$
which simplifies to
$$x = -69$$
6. **Final answer:**
$$\boxed{x = -69}$$