Algebra Lecture Notes

Introduction to Algebra

• Transition from basic math to algebra.
• Algebra is similar to arithmetic but uses symbols, making equations easier to manipulate.

Key Concepts

Variables

• Definition: A variable is a letter or symbol representing a quantity that can change.
• Contrast with Constants: Constants represent quantities that do not change.
• Examples of Variables:
  • Inches of rain in a month
  • Price of gasoline
  • Speed of a plane

Algebraic Expressions

• Composed of numbers, variables, and operations.
• Example: 3x + 2
• Evaluating Expressions:
  • Plug different values into the expression.
  • Example calculations:
    • When x = 1: 3(1) + 2 = 5
    • When x = 2: 3(2) + 2 = 8
    • When x = 3: 3(3) + 2 = 11

Real-World Applications

• Algebraic equations can model real-world situations.
• Example: Cost of cheeseburgers
  • Total cost (Y) = $3 times the number of cheeseburgers (X).

Building Equations

• Example: Watching TV
  • If you watch X hours, Bobo watches twice as much plus one hour.
  • Relationship: Y = 2X + 1

Conclusion

• Algebraic relationships are powerful tools.
• More concepts to learn about algebraic properties in forthcoming discussions.