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Solving Linear Equations and Inequalities: Objectives

Module by: Denny Burzynski, Wade Ellis. E-mail the authors

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Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. In this chapter, the emphasis is on the mechanics of equation solving, which clearly explains how to isolate a variable. The goal is to help the student feel more comfortable with solving applied problems. Ample opportunity is provided for the student to practice translating words to symbols, which is an important part of the "Five-Step Method" of solving applied problems (discussed in modules ((Reference)) and ((Reference))). This module contains the objectives of the chapter "Solving Linear Equations and Inequalities".

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After completing this chapter, you should

Solving Equations ((Reference))

  • be able to identify various types of equations
  • understand the meaning of solutions and equivalent equations
  • be able to solve equations of the form x + a = b x+a=b and x - a = b x-a=b.
  • be familiar with and able to solve literal equation

Solving Equations of the Form ax = b ax=b and x a = b x a =b((Reference))

  • understand the equality property of addition and multiplication
  • be able to solve equations of the form ax = b ax=b and x a = b x a =b

Further Techniques in Equation Solving ((Reference))

  • be comfortable with combining techniques in equation solving
  • be able to recognize identities and contradictions

Applications I - Translating from Verbal to Mathematical Expressions ((Reference))

  • be able to translate from verbal to mathematical expressions

Applications II - Solving Problems ((Reference))

  • be able to solve various applied problems

Linear Inequalities in One Variable ((Reference))

  • understand the meaning of inequalities
  • be able to recognize linear inequalities
  • know, and be able to work with, the algebra of linear inequalities and with compound inequalities

Linear Inequalities in Two Variables ((Reference))

  • be able to identify the solution of a linear equation in two variables
  • know that solutions to linear equations in two variables can be written as ordered pairs

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