Calculator form
Choose an inequality type, enter coefficients, then solve for interval notation and a readable solution statement.
Example data table
| Type | Example input | Solution | Interval notation |
|---|---|---|---|
| Linear | 3x + 4 ≤ x + 10 | x ≤ 3 | (-∞, 3] |
| Compound | -2 ≤ 2x + 3 < 11 | -2.5 ≤ x < 4 | [-2.5, 4) |
| Absolute | |2x - 5| ≥ 7 | x ≤ -1 or x ≥ 6 | (-∞, -1] ∪ [6, ∞) |
Formula used
Linear inequality: Start with ax + b ? cx + d. Rearrange to (a - c)x ? (d - b). Divide by a - c. Reverse the inequality whenever that divisor is negative.
Compound inequality: Solve the left and right statements separately, then intersect both solution sets. A value must satisfy both conditions at the same time.
Absolute value inequality: For |ax + b| ≤ k, rewrite as -k ≤ ax + b ≤ k. For |ax + b| ≥ k, split into ax + b ≤ -k or ax + b ≥ k.
Interval notation: Use parentheses for excluded endpoints and brackets for included endpoints. Join separate valid regions with the union symbol.
How to use this calculator
- Select the inequality type that matches your algebra problem.
- Enter coefficients, constants, operators, and your preferred variable symbol.
- Choose the decimal precision for displayed boundary values.
- Press Solve inequality to generate the result above the form.
- Review the readable solution, interval notation, and worked algebra steps.
- Use the CSV or PDF buttons to save the final result.
FAQs
1. Why does the inequality sign sometimes reverse?
The sign reverses when you divide or multiply both sides by a negative number. This keeps the ordering relationship mathematically correct.
2. What does interval notation mean here?
Interval notation summarizes every valid number in compact form. Parentheses exclude endpoints, while brackets include endpoints.
3. How are compound inequalities solved?
Each side is solved as its own inequality. The final answer is the overlap of both solution sets because both statements must remain true.
4. How are absolute value inequalities handled?
Less than forms become compound inequalities around zero. Greater than forms split into two outer regions and are combined with a union.
5. Can the calculator return no solution?
Yes. If no real number satisfies the inequality, the output shows no real solution and uses the empty set symbol.
6. Can it show all real numbers as a result?
Yes. When every real number satisfies the statement, the tool reports all real numbers and displays the full interval from negative infinity to infinity.
7. Why are some endpoints included and others excluded?
Closed endpoints come from ≤ or ≥ conditions. Open endpoints come from strict < or > conditions.
8. What do the export buttons save?
The export tools save the mode, original problem, readable solution, and interval notation. This makes revision and reporting easier.