Math July 13, 2026 · 8 Min Read

Inequality Calculator – Guide & Formulas

Solve single-variable linear inequalities. Automatically flips signs when multiplying or dividing by negatives and shows interval notation.

Solve standard single-variable linear inequalities (e.g., ax + b < c). Features detailed steps showing operations and when to flip the inequality sign.

Key Takeaway

Use the free Inequality Calculator to solve single-variable linear inequalities. automatically flips signs when multiplying or dividing by negatives and shows interval notation. Get instant results with step-by-step explanations.

How to Use the Inequality Calculator

  1. Select your inequality operator (<, <=, >, >=).
  2. Input the coefficients of your inequality (e.g., ax + b < c).
  3. Check the simplified algebraic solutions, interval notations, and graph representation.

The Formula

ax + b < c => x < (c - b) / a (flips if a is negative)

Variable Definitions

  • a: Coefficient of the variable x
  • b: Constant offset
  • c: Target boundary value

Solving a Negative Rate Inequality

Solve the inequality: -3x + 5 <= 17.

  1. Step 1: Start with -3x + 5 <= 17.
  2. Step 2: Subtract 5 from both sides: -3x <= 12.
  3. Step 3: Divide by -3. CRITICAL: Because we are dividing by a negative number, flip the inequality sign: x >= 12 / -3.
  4. Step 4: Simplify to get x >= -4. In interval notation, this is [-4, ∞).

Frequently Asked Questions

When do you flip the inequality sign?

You must flip the inequality sign whenever you multiply or divide both sides of the inequality by a negative number.

What is the difference between open and closed intervals?

An open interval (using parentheses) does not include the boundary point. A closed interval (using brackets) includes the boundary point (e.g., <= or >=).

How do you represent infinity in interval notation?

Infinity (∞) and negative infinity (-∞) always use parentheses, never brackets, because they are boundaries that cannot be reached.