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Course: Algebra I / Elementary Algebra
Topic: Linear Equations and Inequalities
Subtopic: Solving Linear Equations

Overview

Solving linear equations is one of the most important topics in the entire course especially since the next course concentrates on solving a variety of more complicated equations naturally extending the linear ones studied here. Practice a variety of problems especially those that contain fractions and decimals. Be sure to study the "no solution" and "all solution" special cases too.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 2.1.1 Solve linear equations isolating the x using the "undo property"
• 2.1.2 Solve for x involved in: addition, subtraction, multiplication, division, fractional coefficients
• 2.1.3 Solve for x involved in a combination of operations
• 2.1.4 Solve for x by simplifying first and then isolating
• 2.1.5 Recognize and solve equations that are one of the two "special cases" (no solution, all solutions)
• 2.1.6 Algebraically convert repeating decimal fraction

Terminology

Define: linear vs. nonlinear

Text Notes

Some textbooks use the terms "contradiction" (an equation that has no solution a.k.a. an "inconsistent equation"), "identity" (an equation that is true for all real numbers, i.e. has an infinite number of solutions), and "conditional equation" (which has a finite number of solutions, in fact just one solution when it is a linear conditional equation). I won't use these formal terms, but I do want you to be able to recognize how many solutions an equation has (none, one, two, ..., an infinite number). I prefer to refer to the two "special cases" as "no solution" equations and "all solution" equations. Watch the class discussion boards for examples of each "special case" equation and how to determine if it is no or all solutions.