Inequality Expression Calculator

Analyze linear and compound inequalities using clear inputs and summaries. Review algebraic steps fast instantly. View intervals, graphs, and test points for confident interpretation.

Calculator Inputs

Mode

Variable symbol

Decimal places

Left coefficient

Left constant

Operator

Right coefficient

Right constant

Model used: a₁x + b₁ ? a₂x + b₂

Example Data Table

Case	Input	Output	Interval
Single	3x + 6 ≤ x + 14	x ≤ 4	(-∞, 4]
Single	-2x + 5 > 9	x < -2	(-∞, -2)
Compound	2 ≤ 2x + 1 ≤ 11	0.5 ≤ x ≤ 5	[0.5, 5]
Compound	-3 < x - 4 < 2	1 < x < 6	(1, 6)

Formula Used

a₁x + b₁ ? a₂x + b₂ ⟶ (a₁ - a₂)x ? (b₂ - b₁)

ax + b ? c ⟶ ax ? c - b ⟶ x ? (c - b) / a

If a is negative, reverse the inequality sign after division.

This calculator solves linear inequalities by moving like terms, isolating the variable, reversing the sign only when division uses a negative coefficient, then expressing the answer as inequality notation, interval notation, set-builder form, and a number-line style Plotly graph.

How to Use This Calculator

Choose single inequality for one comparison or compound inequality for a bounded expression.
Enter coefficients and constants exactly as they appear in your algebraic expression.
Pick the inequality symbols carefully because strict and inclusive bounds produce different interval endpoints.
Set decimal precision to control how rounded results appear in the summary and graph.
Press Solve Inequality to view the answer above the form, together with steps, interval notation, test points, and downloadable exports.

FAQs

1. What kinds of inequalities can this page solve?

It solves linear single inequalities and compound inequalities. You can compare one linear expression with another, or place one expression between lower and upper bounds.

2. Why does the sign flip sometimes?

The sign reverses only when you divide or multiply both sides by a negative number. That operation changes the order relationship on the number line.

3. What is interval notation?

Interval notation shows the solution set using brackets and parentheses. Brackets include endpoints, while parentheses exclude them.

4. What does a strict inequality mean?

A strict inequality uses < or >. The boundary value is not included, so the graph marks that point with an open endpoint.

5. Can the calculator return no solution?

Yes. Contradictory statements such as x < 2 and x > 5 together create an empty set, so the final answer becomes no solution.

6. Can the result be all real numbers?

Yes. If simplifying removes the variable and leaves a true statement, every real number satisfies the inequality.

7. Why are test points useful?

Test points help verify whether selected values satisfy the original inequality. They are useful for checking your intuition and spotting sign mistakes.

8. What do the CSV and PDF buttons export?

They export the displayed result summary. This makes it easier to store solutions, share classroom work, or include answers in reports.