Calculator
Supports linear expressions in one variable (default x).
Use
(), +, -, *, /, and implicit multiplication like 2x.Example data
| Type | Input | Solution (interval notation) |
|---|---|---|
| Linear | 2x + 3 <= 11 | (-∞, 4] |
| Linear | (x - 2)/3 > 5 | (17, ∞) |
| Compound (AND) | 2x + 1 >= 0 AND x - 4 < 0 | [-0.5, 4) |
| Absolute value | |3x - 6| <= 9 | [-1, 5] |
Formula used
- Move everything to one side: rewrite L(x) ? R(x) as (L(x) − R(x)) ? 0.
- Standard linear form: reduce the left side to ax + b.
- Divide by the coefficient: if a ≠ 0, solve ax + b ? 0 by dividing by a.
- Flip rule: if you divide by a negative number, reverse the inequality sign.
- Absolute value: |f(x)| ≤ c becomes −c ≤ f(x) ≤ c; and |f(x)| ≥ c becomes f(x) ≥ c or f(x) ≤ −c.
- Compound (AND): solve both inequalities and take the intersection of intervals.
How to use this calculator
- Choose a mode: Linear, Compound, or Absolute value.
- Enter expressions using numbers, the chosen variable, and operators.
- Select the relation sign and submit to solve.
- Read the solution set as interval notation or unions.
- Use CSV or PDF buttons to export the same inputs and result.
Note: The solver supports linear expressions. Products like x*x are rejected.
FAQs
1) What inequalities can this solve?
It solves linear inequalities in one variable, compound AND inequalities, and common absolute value inequalities, producing interval notation with unions when needed.
2) Can I type 2x without the multiplication symbol?
Yes. Implicit multiplication is supported, so 2x, 3(x+1), and (x-2)(3) are interpreted automatically.
3) Why does the sign flip sometimes?
When you divide both sides of an inequality by a negative coefficient, the ordering reverses, so < becomes > and <= becomes >=.
4) What does ∪ mean in the answer?
The symbol ∪ indicates a union of intervals. It appears in cases like |f(x)| > c, where two separate ranges satisfy the inequality.
5) What happens if the variable cancels out?
If the coefficient becomes zero, the inequality reduces to a constant statement like 5 < 0. The result is either “All real numbers” or “No solution,” depending on truth.
6) Does it show exact fractions?
This version formats results as decimals (and scientific notation for extreme values). If you need exact fractions, you can rewrite inputs using fractions like 1/3 and interpret decimals accordingly.
7) Why are nonlinear expressions rejected?
To keep solutions reliable and fast, the parser reduces expressions only to ax + b. Terms like x*x or (x+1)(x-1) produce nonlinear forms and are blocked.
Meta description: Solve inequalities quickly using exact algebra tools. See interval answers with clear boundary markers. Export results as files and share them anywhere online.