Math Problem Statement

∣−b+6∣= 9

Solution

We are given the equation:

b+6=9| -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- b + 6 = 9 Solving for bb: b=96- b = 9 - 6 b=3- b = 3 b=3b = -3

Case 2:

b+6=9- b + 6 = -9 Solving for bb: b=96- b = -9 - 6 b=15- b = -15 b=15b = 15

Thus, the solutions are: b=3orb=15b = -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+6f(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| -b + c | = 9 affect the solution?

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

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Equations

Formulas

| -b + 6 | = 9

Theorems

Absolute Value Theorem

Suitable Grade Level

Grades 7-9