Math Problem Statement

|b/5| = 1

Solution

The given problem is:

b5=1\left|\frac{b}{5}\right| = 1

To solve this, we need to consider the properties of absolute values. The absolute value equation x=1|x| = 1 has two solutions: x=1x = 1 or x=1x = -1. Therefore, the equation can be broken into two parts:

  1. b5=1\frac{b}{5} = 1

    Multiply both sides by 5:

    b=5b = 5

  2. b5=1\frac{b}{5} = -1

    Multiply both sides by 5:

    b=5b = -5

So, the solutions to the equation are:

b=5orb=5b = 5 \quad \text{or} \quad b = -5

Would you like a more detailed explanation or have any questions about this solution?

Related Questions:

  1. How do you solve absolute value equations with more complex expressions?
  2. What happens when the absolute value equals zero, such as b5=0\left|\frac{b}{5}\right| = 0?
  3. How would you graph the function y=b5y = \left|\frac{b}{5}\right|?
  4. What are the general properties of absolute value functions?
  5. Can an absolute value equation have no solution?

Tip: When solving absolute value equations, remember that the equation x=a|x| = a (where a0a \geq 0) always results in two potential cases: x=ax = a and x=ax = -a.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Equations

Formulas

|x| = a has solutions x = a or x = -a

Theorems

Absolute Value Property

Suitable Grade Level

Grades 6-8