To solve the compound inequality $x - 5 < -11$ or $x - 1 \geq -5$, we will solve each part separately.

1. Solve $x - 5 < -11$:

$x - 5 < -11$ Add 5 to both sides: $x < -11 + 5$ $x < -6$

2. Solve $x - 1 \geq -5$:

$x - 1 \geq -5$ Add 1 to both sides: $x \geq -5 + 1$ $x \geq -4$

3. Combine the solutions:

The solution to the compound inequality is the union of the two individual solutions: $x < -6 \quad \text{or} \quad x \geq -4$

So, the solution for $x$ is $x < -6$ or $x \geq -4$.

Would you like more details or have any questions about this solution?

Here are 5 related questions for further practice:

1. Solve the inequality: $2x - 3 < 5$ or $x + 4 \geq 9$.
2. Solve the compound inequality: $3x + 2 > 8$ and $5x - 7 \leq 13$.
3. Solve the inequality: $x - 2 < 4$ or $2x + 1 > 7$.
4. Solve the compound inequality: $4x - 3 \leq 1$ or $x + 2 > 10$.
5. Solve the inequality: $2x + 5 > 9$ or $x - 6 \leq -2$.

Tip: When solving compound inequalities, remember that "or" means you combine the solutions from each part, while "and" means you take the intersection of the solutions.