Glossary
inequality
An inequality compares two expressions with <, >, ≤ or ≥; solve it like an equation, but flip the sign when you multiply or divide by a negative.
An inequality states that one expression is less than, greater than, or at most/at least another, using the symbols < (less than), > (greater than), ≤ (less than or equal to) and ≥ (greater than or equal to). Solve one exactly as you solve an equation: do the same thing to both sides until the variable stands alone. The one new rule is the flip: when you multiply or divide both sides by a negative number, the inequality sign reverses — solving −3x < 12 gives x > −4 (not x < −4). Adding or subtracting never flips the sign, and dividing by a positive never does either. A quick check is to test a number: if the solution says x > 3, then 4 should satisfy the inequality and 2 should not.
Taught in
Related terms
- order of operations — The order of operations is the agreed sequence for evaluating an expression: parentheses, then exponents, then multiply and divide left to right, then add and subtract left to right.
- percent change — A percent change is the amount of change divided by the value you started from, written as a percent: (new − old) ÷ old × 100.
Source: OpenStax Prealgebra, Elementary Algebra and College Algebra, first editions (CC BY 4.0); NIST SP 811 (units). Each definition restates the two Mathematics guides in this exam, which carry the per-source citations on their own pages. (OpenStax 1e and NIST SP 811 accessed 2026-10-07)