inequality math calculator

How to use this inequality math calculator

This calculator solves one-variable linear inequalities quickly and clearly. You enter the values for a, b, the inequality sign, and c in the expression ax + b ? c. The tool then isolates x, flips the inequality sign when needed, and gives you:

• The final inequality solution (example: x ≤ 4)
• Interval notation (example: (-∞, 4])
• Step-by-step algebraic explanation
• An optional check for a test value of x

What is an inequality in math?

An inequality compares two expressions that are not necessarily equal. Instead of using an equals sign, inequalities use:

• < (less than)
• ≤ (less than or equal to)
• > (greater than)
• ≥ (greater than or equal to)

Unlike a single equation answer, inequalities usually describe a range of possible values. For example, x > 5 means any number greater than 5 is a valid solution.

Core rule to remember when solving inequalities

Most algebra steps are the same as equations

You can add, subtract, multiply, or divide both sides by the same number and keep the statement balanced.

One special rule: flip the sign when multiplying or dividing by a negative

This is the most common source of mistakes. If you divide both sides by a negative value, the inequality direction reverses.

Example:

• -2x > 8
• Divide both sides by -2 → x < -4 (sign flips from > to <)

Reading interval notation

After solving, it helps to write the answer in interval form:

• x < a → (-∞, a)
• x ≤ a → (-∞, a]
• x > a → (a, ∞)
• x ≥ a → [a, ∞)

Parentheses mean the endpoint is not included. Brackets mean the endpoint is included.

Quick worked example

Solve: 3x - 5 < 10

1. Add 5 to both sides: 3x < 15
2. Divide by 3: x < 5

Final answer: x < 5, interval notation: (-∞, 5).

Why this calculator is useful

If you are learning algebra, checking homework, or building confidence before exams, this tool helps you verify your logic and catch sign errors. It is especially useful for:

• Algebra 1 and Algebra 2 practice
• SAT, ACT, GED, and placement test prep
• Quick classroom demonstrations
• Self-study and tutoring sessions

Common mistakes this tool helps prevent

• Forgetting to flip the inequality when dividing by a negative number
• Moving constants to the wrong side with incorrect signs
• Confusing open and closed endpoints in interval notation
• Testing values that do not actually satisfy the original inequality

Final tip

After getting the solution, always test one number that should work and one that should not. This habit turns inequality solving from memorization into understanding.