Form: a·x + b ? c. Division by a negative flips the inequality.
Our free Inequality Calculator helps you solve and graph inequalities step-by-step. Enter any linear inequality (like 2x + 5 > 7) or a compound inequality (like -3 ≤ 2x + 1 < 7) and get the solution in:
✅ Set-builder notation
✅ Interval notation
✅ Number line graph
✅ Step-by-step explanation of each algebraic operation
An inequality compares two values or expressions using symbols:
< (less than)
≤ (less than or equal to)
> (greater than)
≥ (greater than or equal to)
For example, 2x + 1 ≥ 5 means “two times x plus one is greater than or equal to five.” The solution is the set of all x values that make the statement true.
<, ≤, >, ≥).{ x > 3 }(3, ∞)The calculator applies standard rules:
Adding/subtracting the same value from both sides keeps the inequality the same.
Multiplying/dividing by a positive number keeps the sign the same.
Multiplying/dividing by a negative number flips the inequality sign.
Example:-2x + 4 ≤ 10
→ Subtract 4 → -2x ≤ 6
→ Divide by -2 (flip sign) → x ≥ -3
Single Inequality:
Solve 2x + 1 < 5 → Subtract 1 → 2x < 4 → Divide by 2 → x < 2
Interval: (-∞, 2)
Compound Inequality:
Solve -3 ≤ 2x + 1 < 7
Break into two parts:-3 ≤ 2x + 1 and 2x + 1 < 7
→ x ≥ -2 and x < 3
Interval: [-2, 3)
Linear inequalities in one variable (ax + b ? c)
Compound inequalities (L ? ax + b ? R)
Strict inequalities (<, >)
Inclusive inequalities (≤, ≥)
Graphical solution on a number line
Q: Can this tool solve compound inequalities?
Yes ✅ — it handles inequalities with two bounds, like -3 ≤ 2x + 1 < 7.
Q: Does the calculator flip the inequality when dividing by a negative?
Yes — the solver automatically flips < to > (and vice versa) when dividing by a negative number.
Q: What notations are supported?
Set-builder form { x ≥ 4 }
Interval notation [4, ∞)
Graphical solution on a number line
Q: Can I graph inequalities?
Yes — the solution is plotted on a number line, showing open or closed endpoints.
Q: Does it handle quadratic inequalities?
This version is for linear and compound inequalities. For quadratic or higher, use a quadratic inequality solver.