1.1 Linear Equations and Rational Equations

Miller & Gerken, College Algebra 2e — Pages 90-103

Learning Objectives

  • Solve linear equations in one variable

  • Solve rational equations by clearing denominators

  • Identify extraneous solutions

  • Recognize conditional, identity, and contradiction equations

Key Concepts

Linear Equation

A linear equation in one variable can be written as:

\[ax + b = 0, \quad a \neq 0\]

Solving Strategy

  1. Clear fractions by multiplying by LCD

  2. Distribute and simplify

  3. Collect variable terms on one side

  4. Isolate the variable

Equation Types

Conditional Equation

Has a finite number of solutions

Identity

True for all values of the variable

Contradiction

No solution (no value makes it true)

Examples

Example 1. Example 1 (p. XX)

Work through textbook example…​

Practice Problems

Problem 1 (p. XX, #YY)

Problem:

My Work:

Answer:

Section Summary

  1. Key point 1

  2. Key point 2

  3. Key point 3

Study Notes

Personal observations and things to remember…​

Next: 1.2 Applications