Inequality Calculator
Solve linear inequalities.
Input
Result
What is an Inequality Calculator?
An inequality calculator solves mathematical inequalities by isolating the variable and applying the correct operations. It handles linear inequalities with <, >, ≤, and ≥ symbols, automatically reversing the sign when multiplying or dividing by a negative number.
How to calculate inequalities manually (the formula)
Treat the inequality like an equation but with an inequality sign. For a linear inequality like ax + b > c, subtract b from both sides, then divide by a. If a is negative, reverse the inequality sign. The solution is a range of values.
Example calculation
Solve 2x + 3 ≤ 11. Subtract 3: 2x ≤ 8. Divide by 2: x ≤ 4. The solution is all numbers less than or equal to 4, written as x ≤ 4 or (−∞, 4].
Common mistakes
- Forgetting to flip the sign — When you multiply or divide by a negative number, the inequality sign must reverse direction.
- Treating inequalities exactly like equations — Inequalities have a range of solutions, not a single value.
- Misreading the inequality symbol — < means 'less than', ≤ means 'less than or equal to'. A closed dot vs. open dot on the graph makes a difference.
Frequently asked questions
What is an inequality?
An inequality compares two values showing if one is less than, greater than, or not equal to another. Common symbols include <, >, ≤, and ≥.
How do you solve a linear inequality?
Isolate the variable on one side using addition, subtraction, multiplication, or division. If you multiply or divide by a negative number, flip the inequality sign.
What is the difference between solving an equation and an inequality?
An equation typically has one solution, while an inequality has a range of solutions. Multiplying or dividing by a negative flips the inequality sign.
How do you graph an inequality on a number line?
Draw an open circle for < or > and a closed circle for ≤ or ≥. Shade in the direction that satisfies the inequality.
Can an inequality have no solution?
Yes. For example, x + 5 < x − 3 simplifies to 5 < −3, which is always false, meaning no value of x satisfies it.
What are compound inequalities?
Compound inequalities combine two inequalities with 'and' or 'or'. 'And' requires both conditions to be true; 'or' requires at least one to be true.