Calculator Form
Build an inequality in the form ax + b [sign] cx + d. The page keeps a clean single-column flow, while the form uses a responsive 3-column, 2-column, and 1-column arrangement.
Example Data Table
| Example | Input Form | Reduced Form | Solution | Interval |
|---|---|---|---|---|
| Example 1 | 2x + 3 ≤ 5x - 6 | -3x ≤ -9 | x ≥ 3 | [3, ∞) |
| Example 2 | -3x + 7 > x - 1 | -4x > -8 | x < 2 | (-∞, 2) |
| Example 3 | 4x - 5 < 4x + 9 | 0 < 14 | All real numbers | (-∞, ∞) |
| Example 4 | 6x + 2 ≥ 6x + 10 | 0 ≥ 8 | No solution | ∅ |
Formula Used
General form: ax + b [sign] cx + d
Rearranged form: (a - c)x [sign] (d - b)
Boundary value: x = (d - b) / (a - c), when a - c ≠ 0
Important rule: Reverse the inequality sign whenever you divide by a negative number.
This calculator simplifies both sides, isolates the variable, converts the answer into interval notation, and draws the solution on a number line. It also handles special cases where the variable cancels completely, producing either all real numbers or no solution.
How to Use This Calculator
- Enter the left coefficient and left constant.
- Select the required inequality sign.
- Enter the right coefficient and right constant.
- Choose a variable label and decimal precision.
- Click Solve Inequality to show the answer above the form.
- Review the reduced form, interval notation, graph direction, and solving steps.
- Use the CSV and PDF buttons to save the result.
FAQs
1. What kind of inequalities does this calculator solve?
It solves linear inequalities written in the form ax + b [sign] cx + d. It supports less than, less than or equal to, greater than, and greater than or equal to comparisons.
2. Why does the inequality sign sometimes change?
The sign reverses when both sides are divided by a negative number. This is a standard algebra rule and keeps the comparison mathematically correct.
3. What does interval notation mean here?
Interval notation describes the full solution set on the number line. Parentheses mean the boundary is excluded, while brackets mean the boundary is included.
4. Can this tool return all real numbers?
Yes. If the variable terms cancel and the remaining statement is always true, the calculator returns all real numbers and graphs the entire number line.
5. Can this tool return no solution?
Yes. If the variable terms cancel and the remaining statement is false, the calculator returns no solution and marks the solution set as empty.
6. Why is the boundary point open or closed?
A closed point appears for ≤ or ≥ because the boundary value is included. An open point appears for < or > because the boundary value is excluded.
7. What is the benefit of changing decimal precision?
Decimal precision controls how many digits appear in rounded answers. It is helpful when the boundary value is not a whole number and you want cleaner output.
8. What do the CSV and PDF buttons export?
The CSV export saves the summary table and solving steps as text data. The PDF export captures the visible result section, including the graph and explanations.