To solve the equation \(|b + 3| - 5 = -2\), let's go through the steps:

1. **Isolate the absolute value expression:**

   \[
   |b + 3| - 5 = -2
   \]

   Add 5 to both sides to isolate the absolute value:

   \[
   |b + 3| = -2 + 5
   \]

   \[
   |b + 3| = 3
   \]

2. **Set up the two possible equations:**

   The absolute value expression \(|b + 3| = 3\) implies two possible cases:
   
   - Case 1: \(b + 3 = 3\)
   - Case 2: \(b + 3 = -3\)

3. **Solve each case:**

   - For Case 1: \(b + 3 = 3\)
     \[
     b = 3 - 3 = 0
     \]

   - For Case 2: \(b + 3 = -3\)
     \[
     b = -3 - 3 = -6
     \]

4. **Final Answer:**

   The solutions to the equation are \(b = 0\) and \(b = -6\).

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you solve an equation with absolute values on both sides?
2. What is the geometric interpretation of absolute value equations?
3. Can absolute value expressions result in negative numbers?
4. How would the solution change if the equation were \(|b + 3| + 5 = 3\)?
5. What if the equation involved \(|b + 3| = b - 3\)?

**Tip:** When dealing with absolute value equations, always consider both the positive and negative cases to find all possible solutions.

Learn how to solve the equation |b + 3| - 5 = -2 step-by-step. This problem involves absolute value equations and linear equations, suitable for Grades 7-9 students learning about solving equations with absolute values.

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