Lesson Notes: Algebraic Expressions & Equations

Lesson Notes:

Introduction to Algebraic Expressions & Equations

Introduction to Algebra

• Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols.
• These symbols represent numbers and are used to describe relationships and changes.

Algebraic Expressions

• An algebraic expression is a mathematical phrase that includes numbers, variables (letters), and operational symbols (+, -, *, /).
• Examples: 3x + 5, 2a - 4, 7y/2

Terms:
Constant: A fixed value, e.g., 5, -3, 7
Variable: A symbol that represents an unknown value, e.g., x, y, a Coefficient: A number multiplied by a variable, e.g., in 3x, 3 is the coefficient Operator: Symbols that represent mathematical operations, e.g., +, -, *, /

Simplifying Algebraic Expressions

• To simplify an algebraic expression, combine like terms.
  Like terms have the same variables raised to the same power. Example: 3x + 4x = 7x (combined like terms)
  Example: 2a + 3b - a + 5b = a + 8b (combined like terms)

Equations

• An equation is a mathematical statement that two expressions are equal. It is written with an equals sign (=).
  Examples: 3x + 5 = 11, 2a - 4 = 10

Solving Equations

• To solve an equation means to find the value of the variable that makes the equation true. Steps to solve a simple linear equation:
  1. Simplify both sides of the equation if needed.

• 2. Use inverse operations to isolate the variable. Example: Solve 3x + 5 = 11
  Step 1: Subtract 5 from both sides: 3x = 6
  Step 2: Divide both sides by 3: x = 2

Types of Equations

• Linear Equations: Equations of the first degree (the highest power of the variable is 1). Example: 2x + 3 = 7
• Quadratic Equations: Equations of the second degree (the highest power of the variable is 2).
• Example: x^2 - 4x + 4 = 0

Application of Algebra in Real Life

• Algebra is used in various fields such as science, engineering, medicine, and economics.

Examples: Calculating distances, determining medication dosages, and solving financial problems.

Summary

• Understanding algebraic expressions and equations is fundamental in mathematics.
• Algebra involves working with variables, constants, coefficients, and operators to form expressions and solve equations.
• Mastering these concepts enables students to tackle more complex mathematical problems and real-world applications.