Calculator
Enter a linear inequality such as 2x + 5 <= 3x - 4, 4(x - 2) > 2x + 6, or 3 - 2x >= 11.
Example data table
| Input inequality | Simplified solution | Interval notation |
|---|---|---|
| 2x + 5 <= 3x - 4 | x >= 9 | [9, ∞) |
| 4(x - 2) > 2x + 6 | x > 7 | (7, ∞) |
| 3 - 2x >= 11 | x <= -4 | (-∞, -4] |
| 5(x + 1) < 20 | x < 3 | (-∞, 3) |
| 2(x + 4) <= 2x + 8 | All real numbers | (-∞, ∞) |
| 3(x - 1) > 3x + 2 | No solution | ∅ |
Formula used
For a linear inequality written as ax + b < cx + d, move variable terms to one side and constants to the other.
Core transformation: ax + b < cx + d → (a - c)x < d - b
Final isolation: x < (d - b) / (a - c) when a - c > 0.
If the coefficient of the variable becomes negative, reverse the inequality sign after division. This sign reversal is the main rule students must remember.
How to use this calculator
- Type a linear inequality using one variable.
- Choose the variable name and output precision.
- Pick interval, set-builder, or both as your preferred view.
- Add an optional test value to verify the solution against the original inequality.
- Press Simplify and solve to see the result section above the form.
- Download the result as CSV or PDF for notes, classwork, or revision records.
FAQs
1. What kinds of inequalities does this calculator support?
It supports linear inequalities with one variable, decimals, parentheses, multiplication by constants, and division by constants. It does not handle quadratic, absolute value, or multi-variable inequalities.
2. Why does the inequality sign sometimes reverse?
The sign reverses when you divide or multiply both sides by a negative number. That preserves truth for the statement and is essential for a correct solution.
3. Can I use fractions inside the inequality?
Yes. Enter fractional ideas using division, such as x/2 + 3 <= 7. The solver treats division by constants correctly and then simplifies the result.
4. What happens if the variable disappears?
The calculator checks whether the remaining statement is true or false. A true statement means all real numbers work. A false statement means there is no solution.
5. What is the difference between interval and set-builder notation?
Interval notation shows the range on the number line, such as (-∞, 4]. Set-builder notation describes the same set using a rule, such as {x | x ≤ 4}.
6. Can I verify a specific number quickly?
Yes. Enter a test value before submitting. The calculator evaluates both sides of the original inequality and reports whether that number satisfies the condition.
7. Does the solver accept uppercase variables?
The variable selector is normalized internally, so a single letter works best. Keep the same chosen letter throughout the inequality to avoid input errors.
8. Why am I seeing an unsupported character error?
That usually means the entry contains symbols outside standard linear notation. Remove extra letters, special math symbols, or unsupported operations, then submit again.