How to Calculate Inequality
What is Inequality?
A linear inequality solver finds all values of x satisfying an inequality like 2x ≤ 10. Unlike equations with one solution, inequalities have a range of solutions, displayed as an interval.
Formula
Linear: ax + b > c ⟹ x > (c−b)/a (if a>0); Quadratic: determine sign across roots using parabola shape
- x
- variable
- a, b, c
- coefficients
Step-by-Step Guide
- 1Solve like an equation, but flip inequality when multiplying/dividing by negative
- 22x ≤ 10 → x ≤ 5
- 3−3x > 6 → x < −2 (flip when dividing by −3)
- 4Represent solution as interval: (−∞, 5]
Worked Examples
Input
2x ≤ 10
Result
x ≤ 5 (interval: (−∞, 5])
Input
−3x > 6
Result
x < −2 (interval: (−∞, −2))
Frequently Asked Questions
What happens to the inequality sign when multiplying by a negative number?
The sign flips! If −x > 5, then x < −5 (reverse the > to <).
How do I solve a compound inequality like 2 < x < 5?
Treat it as two inequalities: 2 < x AND x < 5. Solve each, then find the intersection.
Can I solve quadratic inequalities graphically?
Yes! Sketch the parabola, find roots, and determine where y > 0 or y < 0 based on the shape.
Ready to calculate? Try the free Inequality Calculator
Try it yourself →