To solve the inequality \(-5|x - 1| \geq -20\), follow these steps:

1. **Divide both sides by -5**: 
   Since we are dividing by a negative number, the inequality sign will flip.
   \[
   |x - 1| \leq \frac{-20}{-5}
   \]
   Simplifying this gives:
   \[
   |x - 1| \leq 4
   \]

2. **Interpret the absolute value**:
   The inequality \(|x - 1| \leq 4\) means that the expression \(x - 1\) lies between \(-4\) and \(4\).
   \[
   -4 \leq x - 1 \leq 4
   \]

3. **Solve for \(x\)**:
   Add 1 to all parts of the inequality:
   \[
   -4 + 1 \leq x \leq 4 + 1
   \]
   Simplifying this gives:
   \[
   -3 \leq x \leq 5
   \]

Thus, the solution is \(\boxed{-3 \leq x \leq 5}\).

Would you like further details or have any questions? Here are some related questions:

1. How do you solve inequalities involving absolute values?
2. What happens when you multiply or divide inequalities by a negative number?
3. How do you graph the solution set of an absolute value inequality?
4. What are the common pitfalls when solving inequalities?
5. How do inequalities change when absolute values are involved?

**Tip:** Always remember to flip the inequality sign when multiplying or dividing both sides by a negative number.

Learn how to solve the inequality -5|x - 1| >= -20 with detailed step-by-step instructions. This problem involves inequalities and absolute values, and covers how to interpret absolute values in inequalities. Suitable for students in Grades 9-12.

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