Equation

An equation is a mathematical statement asserting that two expressions have the same value, usually written with an equals sign. It is true for values that make both sides equal.

Mathematical expression: A mathematical expression combines numbers, variables, and operations to represent a value. Each side of an equation is an expression whose value is compared.
Solution of an equation: A solution of an equation is a permitted assignment of values that makes its two sides equal. Solutions are precisely the values that make this equation true.
Linear equation: A linear equation has variables only to the first power and defines a linear constraint. Linear equations are the simplest widely used class of equations.
Inequality: An inequality compares quantities using relations such as less than or greater than rather than equality. It restricts values by comparison instead of asserting equal values.
Equality: Equality is the relation stating that two mathematical objects have the same value or are identical. An equation asserts equality between its left-hand and right-hand expressions.
Solution set: A solution set is the collection of all values satisfying a mathematical condition. It records every value that satisfies an equation, not just one example.
Quadratic equation: A quadratic equation is a polynomial equation of degree two in one variable. Its solutions can be found by factoring, completing the square, or the quadratic formula.
Identity (mathematics): A mathematical identity is an equality that holds for every permitted value of its variables. Unlike a typical equation, an identity is not limited to particular solutions.
Variable: A variable is a symbol representing a quantity that may be unknown or allowed to vary. Variable values often determine whether an equation is true.
Equivalent equations: Equivalent equations have the same solution set over a specified domain. Valid solving steps replace an equation with an equivalent one.

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