You have the inequality:

$x - 1 \geq -6$

To solve this inequality, you need to isolate $x$. Here's the step-by-step solution:

1. Add 1 to both sides of the inequality to eliminate the -1 on the left-hand side: $x - 1 + 1 \geq -6 + 1$

This simplifies to: $x \geq -5$

So, the solution to the inequality is:

$x \geq -5$

Summary:

The inequality $x - 1 \geq -6$ simplifies to $x \geq -5$, which means that $x$ can be any number greater than or equal to $-5$.

Would you like more details or clarification? Let me know!

Here are some related questions for you to explore:

1. How do you solve inequalities with fractions, like $\frac{x}{3} \geq 2$?
2. What happens when the inequality is reversed, like in $x - 1 < -6$?
3. How do you solve absolute value inequalities, like $|x - 3| \leq 4$?
4. What does a solution set look like on a number line for inequalities?
5. How do you graph the solution to $x \geq -5$?

Tip: When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.