Algebra Basics

What is Algebra?

• Algebra is a branch of mathematics that deals with variables and their relationships, often expressed through the use of symbols, equations, and functions.
• It involves the study of mathematical symbols and the rules for manipulating these symbols to solve equations and study structures.

Key Concepts

• Variables: Letters or symbols that represent unknown values or quantities.
• Constants: Numbers that do not change value.
• Algebraic Expressions: Combinations of variables, constants, and mathematical operations.
• Equations: Statements that express the equality of two algebraic expressions.

Types of Algebra

• Elementary Algebra: Deals with solving linear equations and inequalities, graphing lines and functions, and quadratic equations.
• Intermediate Algebra: Covers systems of equations, functions, and graphing, as well as quadratic equations and functions.
• College Algebra: Includes advanced topics such as polynomial and rational functions, sequences and series, and systems of equations.

Algebraic Operations

• Addition: Combining like terms in an algebraic expression.
• Subtraction: Combining like terms with opposite signs.
• Multiplication: Distributing a single value to each term in an algebraic expression.
• Division: Splitting an algebraic expression into two or more equivalent expressions.

Solving Equations

• Linear Equations: Equations in which the highest power of the variable(s) is 1.
• Quadratic Equations: Equations in which the highest power of the variable(s) is 2.
• Systems of Equations: Sets of two or more equations with variables and constants.

Graphing

• Coordinate Plane: A two-dimensional plane with x and y axes.
• Graph of an Equation: A visual representation of the solutions to an equation.
• Functions: Relations between a set of inputs (domain) and a set of possible outputs (range).

What is Algebra?

• Algebra is a branch of mathematics that deals with variables and their relationships, often expressed through symbols, equations, and functions.
• It involves the study of mathematical symbols and the rules for manipulating these symbols to solve equations and study structures.

Key Concepts

• Variables are letters or symbols that represent unknown values or quantities.
• Constants are numbers that do not change value.
• Algebraic expressions are combinations of variables, constants, and mathematical operations.
• Equations are statements that express the equality of two algebraic expressions.

Types of Algebra

• Elementary Algebra deals with solving linear equations and inequalities, graphing lines and functions, and quadratic equations.
• Intermediate Algebra covers systems of equations, functions, and graphing, as well as quadratic equations and functions.
• College Algebra includes advanced topics such as polynomial and rational functions, sequences and series, and systems of equations.

Algebraic Operations

• Addition combines like terms in an algebraic expression.
• Subtraction combines like terms with opposite signs.
• Multiplication distributes a single value to each term in an algebraic expression.
• Division splits an algebraic expression into two or more equivalent expressions.

Solving Equations

• Linear Equations are equations in which the highest power of the variable(s) is 1.
• Quadratic Equations are equations in which the highest power of the variable(s) is 2.
• Systems of Equations are sets of two or more equations with variables and constants.

Graphing

• Coordinate Plane is a two-dimensional plane with x and y axes.
• Graph of an Equation is a visual representation of the solutions to an equation.
• Functions are relations between a set of inputs (domain) and a set of possible outputs (range).