1. What Are Absolute Value Equations?

Absolute value equations are equations that contain an absolute value expression. The absolute value of a number is its distance from zero on the number line, regardless of direction. These equations typically take the form |expression| = k.

2. How Does the Calculator Work?

The calculator uses the absolute value equation principle:

Explanation: For any positive number k, the equation |x| = k has two solutions: x = k and x = -k. The calculator applies this principle to more complex expressions inside the absolute value.

3. Importance of Absolute Value Equations

Details: Absolute value equations are fundamental in algebra and appear in many real-world applications, including distance problems, optimization, and physics problems involving magnitude.

4. Using the Calculator

Tips: Enter your equation in the form |expression| = number. For example: |2x + 3| = 7 or |5 - x/2| = 10. The calculator will show both possible solutions.

5. Frequently Asked Questions (FAQ)

Q1: What if k is negative in |x| = k?
A: Absolute value is always non-negative, so if k is negative, the equation |x| = k has no real solutions.

Q2: What if k is zero in |x| = k?
A: The equation |x| = 0 has exactly one solution: x = 0.

Q3: Can I solve equations like |x + 2| = |x - 5|?
A: This calculator only handles |expression| = k format. For equations with absolute values on both sides, different methods are needed.

Q4: How are more complex absolute value equations solved?
A: For equations like |2x + 3| = x + 1, you would need to consider cases where the expression inside is non-negative and negative.

Q5: Can this calculator handle inequalities?
A: No, this calculator only solves absolute value equations, not inequalities like |x| < 5.