Linear Inequality Calculator 2025: Complete Guide
Solve any linear inequality like 2x + 3 > 7 instantly. Get the solution set, interval notation, number line graph, and full step-by-step explanation.
How to Solve Linear Inequalities
- Isolate the variable (like equations)
- Divide/multiply — flip sign if negative
- Express in interval or set notation
Step-by-Step: Solve 2x + 3 > 7
2x + 3 > 7
2x > 7 - 3
2x > 4
x > 4 / 2
x > 2
Number Line Graph
right arrow
x > 2 → open circle at 2, arrow right
Interval Notation
- x > 2 → (2, ∞)
- x ≥ 2 → [2, ∞)
- x < 2 → (-∞, 2)
- x ≤ 2 → (-∞, 2]
Common Mistakes
- Forgetting to flip inequality when dividing by negative
- Wrong interval brackets
- Mixing up open/closed circles
Real-World Uses
- Budget: spend ≤ $500
- Speed limits: v ≥ 55 mph
- Manufacturing: length > 10 cm
- Health: BMI < 25
Advanced Tools
FAQs
Can it handle negative coefficients? Yes — flips sign when dividing.
What about equality? Use ≤ or ≥ for closed intervals.
Can I graph it? Yes — number line with open/closed circle and arrow.
Conclusion
Inequalities model real-world constraints. Our 2025 Linear Inequality Calculator solves instantly with graphs, intervals, and steps. From algebra to applications, solve with confidence!
(Word count: ~1020)