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, numbers, and operations.
• Examples: 2x + 3, x^2 - 4

Equations and Inequalities

• An equation is a statement that says two expressions are equal.
• Examples: 2x + 3 = 5, x^2 - 4 = 0
• An inequality is a statement that says one expression is greater than, less than, or equal to another.
• Examples: 2x + 3 > 5, x^2 - 4 ≤ 0

Properties of Operations

• Commutative Property: The order of numbers or variables does not change the result.
• Associative Property: The order in which we perform operations does not change the result.
• Distributive Property: Multiplying a single value to multiple terms is the same as multiplying each term separately.

Algebraic Operations:

Simplifying Expressions

• Combining like terms: combining terms with the same variable and coefficient.
• Canceling out terms: eliminating terms that are additive inverses.

Solving Equations and Inequalities

• Adding, subtracting, multiplying, or dividing both sides of an equation or inequality by the same value to isolate the variable.
• Using inverse operations to solve for the variable.

Graphing and Functions

Graphing Equations

• Graphing lines and curves on a coordinate plane to visualize relationships between variables.
• Understanding x-intercepts, y-intercepts, and intercepts of equations.

Functions

• A function is a relation between a set of inputs (domain) and a set of possible outputs (range).
• Domain and range, function notation, and evaluating functions.

Systems of Equations

Substitution Method

• Solving a system of equations by substituting one equation into another.

Elimination Method

• Solving a system of equations by adding or subtracting equations to eliminate one variable.

Quadratic Equations

Factoring

• Factoring quadratic expressions into the product of two binomials.

Quadratic Formula

• Using the formula x = (-b ± √(b^2 - 4ac)) / 2a to solve quadratic equations.

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.

Variables and Expressions

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

Equations and Inequalities

• An equation is a statement that says two expressions are equal.
• Examples of equations: 2x + 3 = 5, x^2 - 4 = 0
• An inequality is a statement that says one expression is greater than, less than, or equal to another.
• Examples of inequalities: 2x + 3 > 5, x^2 - 4 ≤ 0

Properties of Operations

• The Commutative Property states that the order of numbers or variables does not change the result.
• The Associative Property states that the order in which we perform operations does not change the result.
• The Distributive Property states that multiplying a single value to multiple terms is the same as multiplying each term separately.

Algebraic Operations

• Simplifying expressions involves combining like terms and canceling out terms that are additive inverses.
• Algebraic operations can be performed to solve equations and inequalities.

Solving Equations and Inequalities

• Equations and inequalities can be solved by adding, subtracting, multiplying, or dividing both sides by the same value.
• Inverse operations can be used to solve for the variable.

Graphing and Functions

• Graphing equations involves graphing lines and curves on a coordinate plane to visualize relationships between variables.
• X-intercepts, y-intercepts, and intercepts of equations can be used to understand the graph.
• A function is a relation between a set of inputs (domain) and a set of possible outputs (range).
• Domain and range, function notation, and evaluating functions are key concepts in functions.

Systems of Equations

• Systems of equations can be solved using the Substitution Method or the Elimination Method.
• The Substitution Method involves solving one equation and substituting it into another.
• The Elimination Method involves adding or subtracting equations to eliminate one variable.

Quadratic Equations

• Quadratic expressions can be factored into the product of two binomials.
• The Quadratic Formula, x = (-b ± √(b^2 - 4ac)) / 2a, can be used to solve quadratic equations.