Algebra Basics

What is Algebra?

• Algebra is a branch of mathematics that deals with the study of variables and their relationships.
• It involves the use of symbols, equations, and formulas to solve problems and model real-world situations.

Key Concepts

Variables and Expressions

• A variable is a letter or symbol that represents a value that can change.
• An expression is a combination of variables, constants, and mathematical operations.
• Examples: 2x, 3y + 2, x^2 + 4

Equations and Inequalities

• An equation is a statement that says two expressions are equal.
• An inequality is a statement that says two expressions are not equal.
• Examples: 2x + 3 = 5, 4x - 2 > 0

Operations

• Addition and subtraction: combine like terms.
• Multiplication and division: follow the order of operations (PEMDAS).
• Exponentiation: raise a number to a power.

Solving Equations

Linear Equations

• A linear equation is an equation in which the highest power of the variable is 1.
• Examples: 2x + 3 = 5, x - 2 = 0
• Methods: addition, subtraction, multiplication, and division.

Quadratic Equations

• A quadratic equation is an equation in which the highest power of the variable is 2.
• Examples: x^2 + 4x + 4 = 0, x^2 - 4 = 0
• Methods: factoring, quadratic formula.

Graphing

• A graph is a visual representation of an equation or function.
• The x-axis represents the input or independent variable.
• The y-axis represents the output or dependent variable.

Functions

• A function is a relation between a set of inputs and a set of possible outputs.
• Examples: f(x) = 2x, g(x) = x^2 + 1
• Domain: the set of inputs.
• Range: the set of possible outputs.

Systems of Equations

• A system of equations is a set of two or more equations that must be true at the same time.
• Methods: substitution, elimination, and graphical methods.

What is Algebra?

• Algebra is a branch of mathematics that deals with variables and their relationships.
• It involves using symbols, equations, and formulas to solve problems and model real-world situations.

Key Concepts

Variables and Expressions

• A variable is a letter or symbol that represents a value that can change.
• An expression is a combination of variables, constants, and mathematical operations.
• Examples of expressions: 2x, 3y + 2, x^2 + 4

Equations and Inequalities

• An equation is a statement that says two expressions are equal.
• An inequality is a statement that says two expressions are not equal.
• Examples of equations: 2x + 3 = 5
• Examples of inequalities: 4x - 2 > 0

Operations

• Addition and subtraction: combine like terms.
• Multiplication and division: follow the order of operations (PEMDAS).
• Exponentiation: raise a number to a power.

Solving Equations

Linear Equations

• A linear equation is an equation in which the highest power of the variable is 1.
• Examples of linear equations: 2x + 3 = 5, x - 2 = 0
• Methods for solving linear equations: addition, subtraction, multiplication, and division.

Quadratic Equations

• A quadratic equation is an equation in which the highest power of the variable is 2.
• Examples of quadratic equations: x^2 + 4x + 4 = 0, x^2 - 4 = 0
• Methods for solving quadratic equations: factoring, quadratic formula.

Graphing

• A graph is a visual representation of an equation or function.
• The x-axis represents the input or independent variable.
• The y-axis represents the output or dependent variable.

Functions

• A function is a relation between a set of inputs and a set of possible outputs.
• Examples of functions: f(x) = 2x, g(x) = x^2 + 1
• Domain: the set of inputs.
• Range: the set of possible outputs.

Systems of Equations

• A system of equations is a set of two or more equations that must be true at the same time.
• Methods for solving systems of equations: substitution, elimination, and graphical methods.