Enter coefficients and relations to solve inequalities confidently. View interval notation, graphs, and exact bounds. Export results to files and study worked examples quickly.
| Mode | Input | Equivalent solution | Interval notation |
|---|---|---|---|
| Single | 2x + 3 ≤ 11 | x ≤ 4 | (-∞, 4] |
| Single | -3x + 6 > 0 | x < 2 | (-∞, 2) |
| Compound | 2 < 3x + 1 ≤ 13 | 1/3 < x ≤ 4 | (1/3, 4] |
| Combined OR | 2x - 1 ≤ 5 OR x + 4 ≥ 10 | x ≤ 3 or x ≥ 6 | (-∞, 3] ∪ [6, ∞) |
| Combined AND | x + 2 ≥ 1 AND 4x - 8 < 12 | x ≥ -1 and x < 5 | [-1, 5) |
For a standard linear inequality, start with ax + b relation cx + d. Move all x terms to one side and constants to the other side.
The transformed form becomes (a - c)x relation d - b. Then divide by a - c to isolate x.
When dividing by a negative number, reverse the inequality sign. After that, write the answer as interval notation. Use parentheses for open endpoints and brackets for included endpoints.
For compound inequalities, solve each part and keep only the overlap. For OR statements, solve each part and take the union of both intervals.
This calculator helps with single inequalities, compound inequalities, and two separate inequalities joined by AND or OR. It keeps the workflow practical by showing the transformed inequality, the final solution set, and the interval notation in one place.
Interval notation is useful because it compresses long answer statements into a standard mathematical format. An open endpoint means the boundary value is excluded. A closed endpoint means the boundary value is included. Unions let you express split solution sets clearly.
The graph section acts like a number line check. It makes the interval direction, overlaps, and endpoint behavior easier to verify before you copy the answer into homework, notes, or test practice. This is especially useful when a negative coefficient flips the relation sign.
It shows the full solution set on the number line. Parentheses mean an endpoint is excluded. Brackets mean the endpoint is included in the answer.
Reverse the sign only when you multiply or divide both sides by a negative number. That step changes the order relationship on the number line.
Unions are used when the answer has separated parts, such as x ≤ 2 or x > 7. They join both valid intervals into one solution statement.
The result becomes all real numbers, written as (-∞, ∞). That usually happens when the variable cancels and the remaining statement is always true.
The calculator returns the empty set, written as ∅. That occurs when the variable cancels and the remaining statement is false for every real number.
Each side is solved as its own inequality. The final answer is the overlap, because both conditions must hold at the same time.
AND means intersection, so only shared values stay. OR means union, so any value that satisfies either inequality belongs in the solution set.
Yes. It accepts integers and decimals for coefficients, constants, and bounds. The output is still shown as an exact interval-style answer when possible.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.