Display Title
DefinitionEquation ConceptsLinear Equation
Display Title
Definition  Equation Concepts  Linear Equation
This is a collection of definitions related to equations and similar topics. This includes general definitions for equations, as well as terms related to parts of an equation, different types of equations, and characteristics of equations.
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The following section provides additional information on solving one and twostep equations.
Solving OneStep Equations
A onestep equation can literally be solved in one step. This is because the equation is written in a form such that an inverse operation is enough to solve it. Here are the different forms a onestep equation can take:
Equation Type 
Inverse Operation 
Example 
Addition 
Subtraction 

Subtraction 
Addition 

Multiplication 
Division 

Division 
Multiplication 
With these four basic cases, there are a number of variations, depending on the numbers involved. The simplest types of these equations involve positive whole numbers. But these equations can involve integers and rational numbers.
The general form of each of the four types of basic onestep equations are summarized here.
Solving TwoStep Equations
You saw that with onestep equations, the “one step” involved one inverse operation. With twostep equations, there are two inverse operations involved in solving the equation. But this extra step introduces many more types of equations to solve, beyond the basic four from onestep equations.
There are 16 basic types of twostep equations that involve different combinations of the four basic operations.

Addition 
Subtraction 
Multiplication 
Division 
Addition 
AA 
AS 
AM 
AD 
Subtraction 
SA 
SS 
SM 
SD 
Multiplication 
MA 
MS 
MM 
MD 
Division 
DA 
DS 
DM 
DD 
These 16 basic examples are summarized in the table below, where we show an example of such an equation using numbers, then followed by a general form of the equation using variables and constant terms.
Equation Type 
Inverse Operations 
Example 
General Form 
Addition and Addition 
Subtraction and Subtraction 

Addition and Subtraction 
Subtraction and Addition 

Addition and Multiplication 
Subtraction and Division 

Addition and Division 
Subtraction and Multiplication 

Subtraction and Addition 
Addition and Subtraction 

Subtraction and Subtraction 
Addition and Addition 

Subtraction and Multiplication 
Addition and Division 

Subtraction and Division 
Addition and Multiplication 

Multiplication and Addition 
Division and Subtraction 

Multiplication and Subtraction 
Division and Addition 

Multiplication and Multiplication 
Division and Division 

Multiplication and Division 
Division and Multiplication 

Division and Addition 
Multiplication and Subtraction 

Division and Subtraction 
Multiplication and Addition 

Division and Multiplication 
Multiplication and Division 

Division and Division 
Multiplication and Multiplication 
These 16 basic twostep equations come in different forms depending on the sign of the numbers and whether the numbers are integers or rational numbers. The simplest types of these equations involve positive whole numbers.
Equation Type 
General Form 
Addition 

Subtraction 

Multiplication 

Division 

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Common Core Standards  CCSS.MATH.CONTENT.6.EE.B.5, CCSS.MATH.CONTENT.7.EE.B.4, CCSS.MATH.CONTENT.HSA.REI.A.1 

Grade Range  6  12 
Curriculum Nodes 
Algebra • Linear Functions and Equations • Applications of Linear Functions 
Copyright Year  2021 
Keywords  equations, solving equations, definitions, glossary terms 