Algebra Basics

Algebra

What is Algebra?

• Branch of mathematics that deals with variables and their relationships
• Involves the study of symbols, equations, and functions to solve problems

Key Concepts:

1. Variables and Expressions

• A variable is a symbol that represents a value that can change
• An expression is a group of variables, numbers, and operations combined using mathematical operations (+, -, x, /)

2. Equations and Inequalities

• An equation is a statement that says two expressions are equal (e.g., 2x + 3 = 5)
• An inequality is a statement that compares two expressions using <, >, ≤, or ≥ (e.g., 2x - 4 > 0)

3. Linear Equations

• A linear equation is an equation in which the highest power of the variable(s) is 1
• Can be written in the form: ax + by = c, where a, b, and c are constants

4. Quadratic Equations

• A quadratic equation is an equation of degree 2, written in the form: ax^2 + bx + c = 0
• Can be solved using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

5. Functions

• A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range)
• Can be represented algebraically, graphically, or numerically

6. Graphing

• Graphing involves plotting points on a coordinate plane to visualize relationships between variables
• Types of graphs: linear, quadratic, exponential, and more

7. Systems of Equations

• A system of equations is a set of two or more equations with variables in common
• Can be solved using substitution, elimination, or matrices

Algebra

What is Algebra?

• Algebra is a branch of mathematics that deals with variables and their relationships
• It involves the study of symbols, equations, and functions to solve problems

Key Concepts:

Variables and Expressions

• A variable is a symbol that represents a value that can change
• An expression is a group of variables, numbers, and operations combined using mathematical operations (+, -, x, /)

Equations and Inequalities

• An equation is a statement that says two expressions are equal (e.g., 2x + 3 = 5)
• An inequality is a statement that compares two expressions using , ≤, or ≥ (e.g., 2x - 4 > 0)

Linear Equations

• A linear equation is an equation in which the highest power of the variable(s) is 1
• Can be written in the form: ax + by = c, where a, b, and c are constants

Quadratic Equations

• A quadratic equation is an equation of degree 2, written in the form: ax^2 + bx + c = 0
• Can be solved using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

Functions

• A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range)
• Can be represented algebraically, graphically, or numerically

Graphing

• Graphing involves plotting points on a coordinate plane to visualize relationships between variables
• Types of graphs: linear, quadratic, exponential, and more

Systems of Equations

• A system of equations is a set of two or more equations with variables in common
• Can be solved using substitution, elimination, or matrices