Let's solve the inequality:

$|9b - 900| \leq -900$

Step 1: Analyze the inequality

The absolute value function, $|9b - 900|$, always produces a non-negative result (i.e., a value greater than or equal to 0). However, on the right side of the inequality, we have $-900$, which is negative.

Since an absolute value expression can never be less than a negative number, this inequality has no solution. There is no value of $b$ that will satisfy this inequality because the absolute value on the left cannot be negative.

Step 2: Graphical Interpretation

Since the inequality has no solution, there is no portion of the number line to graph. Therefore, the graph would be empty. No line or ray will be shown because there are no values for $b$ that satisfy the condition.

---

Would you like me to explain further or help with a different problem?

Here are five related questions for further learning:

1. How do absolute value inequalities work when the right side is non-negative?
2. How do you solve an inequality with absolute values?
3. What happens when the absolute value expression is greater than a negative number?
4. How do we graph solutions for absolute value inequalities on a number line?
5. What is the general method for solving absolute value equations vs. inequalities?

Tip: Whenever solving absolute value inequalities, make sure to first assess if the inequality's right side is non-negative, as absolute value expressions cannot be less than a negative number.