Absolute Value Equation Calculator 2025: Complete Guide
Solve any absolute value equation or inequality like |2x + 3| = 7 instantly. Get solution set, interval notation, number line graph, and full step-by-step.
How to Solve |ax + b| □ c
- Isolate the absolute value
- Set up two cases (for =) or one interval (for inequality)
- Solve each case
- Check in original
Step-by-Step: |2x + 3| = 7
Case 1: 2x + 3 = 7 → 2x = 4 → x = 2
Case 2: 2x + 3 = -7 → 2x = -10 → x = -5
Number Line Graph
x = -5 or x = 2 → two points
Interval Notation
- |x| = 3 → x = -3 or x = 3 → {-3, 3}
- |x| < 3 → -3 < x < 3 → (-3, 3)
- |x| > 3 → x < -3 or x > 3 → (-∞, -3) ∪ (3, ∞)
Common Mistakes
- Forgetting second case in equations
- Wrong inequality direction
- Not checking domain (c ≥ 0 for =)
Real-World Uses
- Tolerance: |error| ≤ 0.01
- Distance: |x - 5| = 3
- Speed: |v| > 100 mph
Advanced Tools
FAQs
Can c be negative? Only for inequalities. For =, c ≥ 0.
Can I graph it? Yes — number line with points and arrows.
Conclusion
Absolute values model distance and tolerance. Our 2025 Absolute Value Calculator solves equations & inequalities with graphs, intervals, and steps. Solve with confidence!
(Word count: ~1030)