We are given the equation:

\[
| -b + 6 | = 9
\]

To solve this, we need to break it into two possible cases since the absolute value function can yield two different results (positive and negative):

### Case 1: 
\[
- b + 6 = 9
\]
Solving for \( b \):
\[
- b = 9 - 6
\]
\[
- b = 3
\]
\[
b = -3
\]

### Case 2: 
\[
- b + 6 = -9
\]
Solving for \( b \):
\[
- b = -9 - 6
\]
\[
- b = -15
\]
\[
b = 15
\]

Thus, the solutions are:
\[
b = -3 \quad \text{or} \quad b = 15
\]

Would you like more details or have any questions?  
Here are 5 related questions to deepen your understanding:
1. What happens when an absolute value equation has no solutions?
2. How would this change if the absolute value was less than 9 instead of equal to 9?
3. Can you graph the function \( f(b) = | -b + 6 | \) and observe its behavior?
4. What are the steps to solving an absolute value inequality?
5. How does changing the constant in the equation \( | -b + c | = 9 \) affect the solution?

**Tip:** Always remember that absolute value equations can have two cases, as it represents distance from zero.

Learn how to solve the absolute value equation | -b + 6 | = 9 step-by-step. This guide breaks down the problem into two cases, explains the process for solving each, and covers key algebraic concepts. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation