Inequality Calculator

A linear inequality is like a linear equation, but instead of an equals sign it uses an inequality symbol: >, <, ≥, or ≤.

Solving Linear Inequalities:

The process is the same as solving equations, with one critical rule: if you multiply or divide both sides by a negative number, flip the inequality sign.

Worked Example:

Solve -3x + 7 ≥ 1.

1. Subtract 7 from both sides: -3x ≥ -6
2. Divide both sides by -3 (flip the sign): x ≤ 2
3. Interval notation: (-∞, 2]
4. Number line: closed dot at 2, shade to the left.

Interval Notation:

• (a, b) means a < x < b (endpoints not included)
• [a, b] means a ≤ x ≤ b (endpoints included)
• (-∞, a) means x < a
• [a, ∞) means x ≥ a
• Always use parentheses (not brackets) next to infinity.

Number Line Representation:

• Open dot = endpoint not included (strict inequality)
• Closed/filled dot = endpoint included (≤ or ≥)
• Shading indicates which direction contains the solutions.