Equations and Inequalities
An equation states that two expressions are equal, while an inequality relates two different values.
Learning Objective

Differentiate between the basic properties of equations and inequalities
Key Points
 An equation is a mathematical statement that asserts the equality of two expressions.
 An inequality is a relation that holds between two values when they are different.
 The notation
$a \neq b$ means that$a$ is not equal to$b$ . It does not say that one is greater than the other, or even that they can be compared in size. If one were to compare the size of the values, the notation$a < b$ means that$a$ is less than$b$ , while the notation$a > b$ means that$a$ is greater than$b$ .
Terms

equation
An assertion that two expressions are equal, expressed by writing the two expressions separated by an equals sign. E.g.,
$x=5$ . 
inequality
A statement that of two quantities one is specifically less than or greater than another. Symbols:
$\leq$ or$\geq$ , as appropriate. 
unknown
A variable (usually
$x$ ,$y,$ or$z$ ) whose value is to be found.
Example
$x+3=5$ asserts that$x+3$ is equal to$5$ .
Full Text
Equations
An equation is a mathematical statement that asserts the equality of two expressions. This is written by placing the expressions on either side of an equals sign (=), for example:
asserts that
Equation as a Balance
Illustration of a simple equation as a balance.
Equations often express relationships between given quantities—the knowns—and quantities yet to be determined—the unknowns. By convention, unknowns are denoted by letters at the end of the alphabet (
Inequalities
An inequality is a relation that holds between two values when they are different. The notation
In either case,
 The notation
$a < b$ means that a is less than$b$ . (It may also be read as "a is strictly less than$b$ ".)  The notation
$a > b$ means that a is greater than$b$ .
In contrast to strict inequalities, there are two types of inequality relations that are not strict:
 The notation
$a \leq b$ means that$a$ is less than or equal to$b$ (or, equivalently, not greater than$b$ , or at most$b$ ).  The notation
$a \geq b$ means that$a$ is greater than or equal to$b$ (or, equivalently, not less than$b$ , or at least$b$ ).
Key Term Reference
 equality
 Appears in these related concepts: The Trial Balance, Inputs to Accounting, and Solving Equations: Addition and Multiplication Properties of Equality
 expression
 Appears in these related concepts: Compound Inequalities, Sets of Numbers, and Simplifying, Multiplying, and Dividing
 relation
 Appears in these related concepts: Functions and Their Notation, Symmetry of Functions, and What is a Linear Function?
 root
 Appears in these related concepts: Introduction to Radicals, The Rule of Signs, and Zeroes of Polynomial Functions with Real Coefficients
 set
 Appears in these related concepts: Sequences, Introduction to Sequences, and Executive Function and Control
 sign
 Appears in these related concepts: Polynomial Inequalities, The Intermediate Value Theorem, and Sequences of Mathematical Statements
 system of equations
 Appears in these related concepts: Nonlinear Systems of Inequalities, Applications of Systems of Equations, and Models Involving Nonlinear Systems of Equations
 term
 Appears in these related concepts: Basics of Graphing Polynomial Functions, The 22nd Amendment, and Introduction to Variables
Sources
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