Solve Linear Inequalities Calculator

Calculator form

Enter the inequality in the form ax + b ? cx + d. The page layout is single column, while the inputs use a responsive 3-2-1 grid.

Left coefficient (a)

Left constant (b)

Inequality symbol

Right coefficient (c)

Right constant (d)

Variable letter

Decimal precision

Example data table

a	b	Symbol	c	d	Inequality	Solution
2	3	<	0	11	2x + 3 < 11	x < 4
-1	5	>=	2	8	-x + 5 >= 2x + 8	x <= -1
3	-9	<=	3	1	3x - 9 <= 3x + 1	All real numbers
4	2	>	4	10	4x + 2 > 4x + 10	No solution

Formula used

Start from a one-variable linear inequality written as ax + b ? cx + d.

Move variable terms to one side: (a - c)x ? d - b
If a - c > 0, divide normally and keep the sign.
If a - c < 0, divide and reverse the inequality sign.
If a - c = 0, the variable cancels. Then test whether the remaining statement is always true or always false.

This method works for <, <=, >, and >= inequalities with real-number coefficients.

How to use this calculator

Enter the left coefficient and left constant.
Choose the inequality symbol you want to solve.
Enter the right coefficient and right constant.
Select the variable letter and preferred decimal precision.
Press Solve Inequality to place the result above the form.
Review the reduced form, final answer, interval notation, and test points.
Use the graph to see which side of the boundary belongs to the solution set.
Download a CSV or PDF copy of the computed result.

FAQs

1) What kind of inequalities does this page solve?

It solves one-variable linear inequalities written in the form ax + b ? cx + d. It supports less than, less than or equal to, greater than, and greater than or equal to symbols.

2) Why does the sign flip after dividing sometimes?

The sign flips only when you divide or multiply both sides by a negative number. That operation reverses the order on the number line, so the inequality direction must reverse too.

3) What does interval notation mean here?

Interval notation is a compact way to show the full solution set. Parentheses exclude a boundary value, while square brackets include it. Infinity always uses parentheses.

4) What happens if the variable cancels out?

When variable terms cancel, the calculator checks the remaining numeric statement. If that statement is true, every real number is a solution. If false, there is no solution.

5) Can I use decimals and negative numbers?

Yes. The calculator accepts decimals, negative coefficients, negative constants, and zero values. Precision controls only the displayed rounding, not the algebraic solving logic.

6) What do the test points show?

The test points evaluate values on both sides of the boundary. They help confirm which side of the number line satisfies the original inequality and whether the boundary is included.

7) Why might I get no solution?

You get no solution when the inequality simplifies to a false statement, such as 2 > 5, or when the final algebra leaves a region with no real values satisfying the condition.

8) Are the downloads useful for teachers and students?

Yes. CSV files are handy for logs and worksheets, while PDF files are useful for printouts, homework review, tutoring notes, and classroom demonstrations.