Math Problem Statement
∣−b+6∣= 9
Solution
We are given the equation:
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:
Solving for :
Case 2:
Solving for :
Thus, the solutions are:
Would you like more details or have any questions?
Here are 5 related questions to deepen your understanding:
- What happens when an absolute value equation has no solutions?
- How would this change if the absolute value was less than 9 instead of equal to 9?
- Can you graph the function and observe its behavior?
- What are the steps to solving an absolute value inequality?
- How does changing the constant in the equation affect the solution?
Tip: Always remember that absolute value equations can have two cases, as it represents distance from zero.
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Equations
Formulas
| -b + 6 | = 9
Theorems
Absolute Value Theorem
Suitable Grade Level
Grades 7-9