What is an Equation?
In an equation with one variable, the variable has a solution, or value, that makes the equation true.
Learning Objective

Explain what an equation in one variable represents and the reasons for using one
Key Points
 An equation is a mathematical statement that asserts the equivalence of two expressions.
 When an equation contains a variable, such as
$x$ , the variable is considered an unknown value.  The values of the variables that make the equation true are the solutions of the equation and can be found by solving the equation.
 A solution of an equation can be verified, or checked, by substituting in its value for the variable in the equation.
Terms

solution
A value that can be substituted for a variable to make an equation true.

unknown
A variable in an equation that needs to be solved for.

equation
A mathematical statement that asserts the equivalence of two expressions.
Full Text
An
equation is a mathematical statement that asserts the equivalence of two
expressions. For example, the assertion that "two plus five equals seven" is represented by the equation
In many cases, an equation contains one or more variables. These are still written by placing each expression on either side
of an equals sign (
It is possible for equations to have more than one variable. For example,
Solving Equations
When an equation contains a variable such as
For example, consider the equation we were talking about above:
The values of the variables that make an equation true are called the solutions of the equation. In turn, solving an equation means determining what values for the variables make the equation a true statement.
The equation above was fairly straightforward; it was easy for us to identify the solution as
Verifying Solutions
If a number is found as a solution to an equation, then substituting that number back into the place of the variable should make the equation true. Thus, we can easily check whether a number is a genuine solution to a given equation.
For example, let's examine whether
Substituting 3 for
This equality is a true statement. Therefore, we can conclude that
Key Term Reference
 complex
 Appears in these related concepts: Transduction of Sound, Introduction to Complex Numbers, and Electron Transport Chain
 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
 sign
 Appears in these related concepts: Polynomial Inequalities, The Intermediate Value Theorem, and The Rule of Signs
 variable
 Appears in these related concepts: What is a Linear Function?, Math Review, and Introduction to Variables
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