We are asked to solve the inequality $-6a - 11 \leq -(a + 6)$.

1. Problem Description

We are asked to solve the inequality $-6a - 11 \leq -(a + 6)$.

2. Solution Steps

First, distribute the negative sign on the right side of the inequality:

$-6a - 11 \leq -a - 6$

Next, add $a$ to both sides of the inequality:

$-6a - 11 + a \leq -a - 6 + a$

$-5a - 11 \leq -6$

Add 11 to both sides:

$-5a - 11 + 11 \leq -6 + 11$

$-5a \leq 5$

Divide both sides by -

5. Remember to flip the inequality sign when dividing by a negative number:

$\frac{-5a}{-5} \geq \frac{5}{-5}$

$a \geq -1$

3. Final Answer

$a \geq -1$