Compound Inequality Calculator

Solve compound inequalities of the form L < ax + b < U or L ≤ ax + b ≤ U.

InequalitiesAlgebraHigh School Math

Calculator

Lower bound L
a
b
Upper bound U
Inequality type
Please enter valid values.

What this calculator teaches

Compound inequalities restrict a variable between two boundaries.

The key move is doing the same operation to all three parts, and reversing signs when dividing by a negative number.

Formula & Symbols

ConceptFormulaMeaning
Open compound inequalityLEndpoint values are not included.
Closed compound inequalityL≤ax+b≤UEndpoint values are included.

Step-by-Step Examples

Example 1
Solve 1 < 2x+3 < 11
  • Subtract 3 from all parts: -2 < 2x < 8.
  • Divide all parts by 2.
✓ -1 < x < 4.

Where students use this

🎓
High school and college
Use the calculator to check homework and understand each step.
📊
Modeling and data
Connect formulas to tables, graphs, and real values.
🧪
Science and engineering
Use the result inside physics, chemistry, engineering, and lab problems.
💻
Computer science
Apply the same math to algorithms, simulations, and numerical work.

Common Mistakes to Avoid

⚠️
Mixing notation with calculator input

Mathematical notation is compact, but calculators need explicit numbers and operators.

⚠️
Skipping domain restrictions

Some formulas only work when denominators are nonzero, logs have positive inputs, and square roots are valid.

⚠️
Rounding too early

Keep extra decimals while solving and round only the final answer.

Frequently Asked Questions

Is this calculator for learning or only answers?
It is designed for both. The result panel gives the answer, while the examples and explanation show why the method works.
Can I use decimals and negatives?
Yes, unless the specific topic has a restriction such as a positive base, positive radicand, or nonzero denominator.
Why might my answer differ from a textbook?
Different rounding, equivalent algebraic forms, or a different interpretation of the input can produce a different-looking but equivalent result.
Does this replace solving by hand?
No. It helps verify work and understand the steps, but students should still practice the method manually.

Related Math Calculators

Formula Explorer connections

Interpretation: This formula describes an algebraic relationship among variables, functions, equations, roots or sequences. Assumption: Respect the expression’s domain and excluded values. Check roots in the original equation because transformations can introduce extraneous solutions.

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