Calculator form
Enter a linear inequality in the form ax + b ? cx + d. Results appear above this form after submission.
Example data table
| Example | Inequality | Reduced form | Solution | Interval |
|---|---|---|---|---|
| 1 | 2x + 3 > x + 7 | x > 4 | x > 4 | (4, ∞) |
| 2 | 4x - 5 ≤ 2x + 9 | 2x ≤ 14 | x ≤ 7 | (-∞, 7] |
| 3 | -3x + 6 ≥ x - 10 | -4x ≥ -16 | x ≤ 4 | (-∞, 4] |
| 4 | 5x + 1 < 5x + 9 | 0 < 8 | All real numbers | (-∞, ∞) |
Formula used
General form: ax + b ? cx + d
Rearrange: (a - c)x ? (d - b)
Solve: x ? (d - b) / (a - c)
Important rule: Reverse the inequality sign when you divide or multiply both sides by a negative number.
How to use this calculator
- Enter the left coefficient and constant.
- Select the correct inequality sign.
- Enter the right coefficient and constant.
- Choose your decimal precision and graph padding.
- Press Solve inequality to calculate the answer.
- Review the result, interval notation, steps, and graph.
- Download the output as CSV or PDF when needed.
FAQs
1) Can I use decimals in the inequality?
Yes. The calculator accepts decimals for every coefficient and constant. It solves the resulting linear inequality and shows the decimal boundary value using your chosen precision.
2) Why does the inequality sign sometimes flip?
When you divide or multiply by a negative number, the inequality direction reverses. The steps section shows exactly when that change happens.
3) What happens if the x-terms cancel?
If the x-terms cancel, the inequality becomes a constant statement. The result is either all real numbers or no solution, depending on whether the statement is true.
4) What is interval notation?
Interval notation writes the solution set compactly. For example, x > 3 becomes (3, ∞), while x ≤ 3 becomes (-∞, 3].
5) What do open and closed circles mean?
An open circle means the boundary value is excluded. A closed circle means the boundary value is included in the solution set.
6) What does the graph represent?
The graph is a number line view of the solution. It helps you see whether values to the left or right of the boundary satisfy the inequality.
7) Can I export my answer?
Yes. Use the CSV button for structured data export. Use the PDF button to save the result summary, steps, and graph as a report.
8) Does this page solve every kind of inequality?
This page solves linear inequalities in one variable. It does not solve quadratic, absolute value, or system-based inequalities.