Inequality Calculator
Solve inequality problems step-by-step with our free calculator. See formulas, worked examples, and clear explanations.
Formula
ax + b < cx + d (solve for x)
Enter the coefficients and constants for both sides of the inequality. The calculator moves all variable terms to one side and constants to the other, then divides by the coefficient. If dividing by a negative number, the inequality sign is automatically flipped.
Worked Examples
Example 1: Basic Linear Inequality
Problem: Solve the inequality: 3x - 7 < 5x + 2
Solution: Move all x terms to left side: 3x - 5x < 2 + 7\nSimplify: -2x < 9\nDivide by -2 (flip the sign): x > -4.5\nInterval notation: (-4.5, Infinity)\nTest: x = 0 gives 3(0) - 7 = -7 < 5(0) + 2 = 2, which is true.
Result: x > -4.5 or (-4.5, Infinity)
Example 2: Inequality with Equal Coefficients
Problem: Solve: 4x + 3 <= 4x + 8
Solution: Subtract 4x from both sides: 3 <= 8\nThis is always true.\nThe x terms cancel out, leaving a true numerical statement.\nTherefore the solution is all real numbers.\nInterval notation: (-Infinity, Infinity)
Result: All real numbers: (-Infinity, Infinity)
Frequently Asked Questions
What is an inequality and how does it differ from an equation?
An inequality is a mathematical statement that compares two expressions using inequality symbols such as less than, greater than, less than or equal to, or greater than or equal to. Unlike equations which have specific solutions, inequalities typically have a range of solutions. For example, x > 3 means any value greater than 3 satisfies the inequality, giving infinitely many solutions. Equations use the equals sign and find exact values, while inequalities define regions on the number line. Understanding this distinction is crucial because many real-world problems involve constraints and ranges rather than exact values.
Is Inequality Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.
Does Inequality Calculator work offline?
Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.
Can I use Inequality Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.