Advanced Inequality Value Calculator

Analyze linear inequalities confidently with instant interval notation and visual verification. Compare both sides precisely. Get accurate solutions, graphs, and exports for deeper practice.

Calculator Input

Enter values for the inequality form ax + b [relation] cx + d.

Left Coefficient (a)

Value multiplying x on the left side.

Left Constant (b)

Constant added on the left side.

Inequality Relation

Choose the comparison sign to solve.

Right Coefficient (c)

Value multiplying x on the right side.

Right Constant (d)

Constant added on the right side.

Graph Minimum x

Lower bound for the graph window.

Graph Maximum x

Upper bound for the graph window.

Reset

Example Data Table

a	b	Relation	c	d	Simplified Form	Solution	Interval
2	5	≤	3	11	-x ≤ 6	x ≥ -6	[-6, ∞)
4	-3	>	1	9	3x > 12	x > 4	(4, ∞)
1	7	<	1	9	0 < 2	All real numbers	(-∞, ∞)

Formula Used

General form: ax + b [relation] cx + d

Rearrange terms: (a - c)x [relation] (d - b)

If (a - c) > 0: x [same relation] (d - b) / (a - c)

If (a - c) < 0: x [reversed relation] (d - b) / (a - c)

If (a - c) = 0: test whether 0 [relation] (d - b) is always true or always false.

How To Use This Calculator

Enter the left coefficient and constant for the first expression.
Choose the inequality symbol that matches your problem.
Enter the right coefficient and constant for the second expression.
Set a graph minimum and maximum x value for visual analysis.
Press Solve Inequality to display the result above the form.
Review the isolated solution, interval notation, and set-builder output.
Use the sample check table to verify satisfying and non-satisfying x values.
Download the result summary as CSV or PDF whenever needed.

FAQs

1) What inequality types can this calculator solve?

It solves linear inequalities written as ax + b compared with cx + d. You can use less than, less than or equal to, greater than, and greater than or equal to signs.

2) When does the inequality sign reverse?

The sign reverses only when you divide or multiply both sides by a negative number. In this calculator, that happens when the combined x coefficient after rearranging is negative.

3) What does interval notation mean here?

Interval notation shows every valid x value in a compact form. Parentheses mean the boundary is excluded, while brackets mean the boundary value is included in the solution.

4) Why do some inputs return all real numbers?

That happens when the x terms cancel out and the remaining statement is always true, such as 0 < 4 or 0 ≤ 0. Every real x then satisfies the inequality.

5) Why can the calculator show no solution?

No solution appears when the x terms cancel out and the remaining statement is false, such as 0 > 5 or 0 < -2. No real x can make it true.

6) How does the graph help with understanding?

The graph plots both expressions against x. Their crossing point gives the boundary, and the highlighted side shows where the chosen inequality condition is satisfied.

7) Can I use decimals and negative values?

Yes. The inputs accept decimals, negative numbers, and zero. That makes the tool suitable for classroom exercises, homework, and quick verification tasks.

8) What is included in the CSV and PDF exports?

The exports include the original inequality, simplified steps, final solution, boundary value, interval notation, and the sample validation table shown in the result section.