Learning Objectives
Introduction
No matter what type of equation you are working with in this section, the ultimate goal is to get your variable on one side and everything else on the other side using inverse operations.
Tutorial
If you need a review on finding the LCD of a rational expression, go to Tutorial 10: Adding and Subtracting Rational Expressions.
Note that even though this is not the same as adding and subtracting
rational expressions, you still find the LCD in the same manner. So
if you go to this link, just look at finding the LCD, NOT adding and subtracting
rational expressions.
Step 2: Solve the
remaining equation.
If you need a review on solving linear equations go back to Tutorial
14: Linear Equations.
Step 3: Check for
extraneous solutions.
In Tutorial
14: Linear Equations, I told you that when you multiply both sides
by the same constant that the two sides would remain equal to each other.
But we can not guarantee that if you are multiplying by an expression that
has the variable you are solving for - which is the situation we will be
running into in this section. Sometimes this will cause extraneous
solutions.
Example
1: Solve for y.
*Inverse of mult. by -1 is div. by -1
9 is the solution to our equation.
Example
2: Solve for a.
*Factor 1st den.
*Mult.
both sides by LCDof (a + 3)(a - 2)
*Get all a terms
on one side
*Inverse of add. 8 is sub. 8
7 is the solution to our equation.
Example
3: Solve for x.
*Inverse of add. 9 is sub. 9
*Inverse of mult. by -1 is div. by -1
So 3 is an extraneous solution. That means there is no solution.
The answer is NO solution.
Practice Problems
To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that problem. At the link you will find the answer as well as any steps that went into finding that answer.
Practice Problems 1a - 1b: Solve the given equation.
Need Extra Help on these Topics?
Go to Get Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for some
more suggestions.
Videos at this site were created and produced by Kim Seward and Virginia Williams Trice.
Last revised on Dec 16, 2009 by Kim Seward.
All contents copyright (C) 2002 - 2010, WTAMU and Kim Seward.
All rights reserved.