**Learning Objectives**

After completing this tutorial, you should be able to:

- Solve linear equations by using a combination of simplifying and using various properties of equality.

** Introduction**

In **Tutorial 12:
The Addition Property
of Equality** we looked at using the addition property of
equality
to help us solve linear equations. In **Tutorial
13: The Multiplication Property of Equality** we looked at using
the multiplication property of equality and also put these two ideas
together.
In this tutorial we will be solving linear equations by using a
combination
of simplifying and various properties of equality.

Knowing how to solve linear equations will open the door
to being able
to work a lot of other types of problems that you will encounter in
your
various algebra classes. **It is very important to have this
concept
down before moving ahead.** Make sure that you do not savor the
mystery of finding your variable, but work through some of these types
of problems until you have this concept down.

** Tutorial**

**Step 1: Simplify each side, if needed.**

This would involve things like removing ( ),
removing fractions, removing
decimals, and adding like terms.

**To remove ( ): ** Just use the **distributive
property found in Tutorial 8: Properties of Real Numbers.**

**To remove fractions**: Since fractions are
another way to write
division, and the inverse of divide is to multiply, you remove
fractions
by multiplying both sides by the LCD of all of your fractions. If
you need a **review on the
LCD,
go to Tutorial 3: Fractions.**

Step 2: Use Add./Sub. Properties to
move the variable
term to one side and all other terms to the other side.

**Step 3: Use Mult./Div. Properties to
remove any values
that are in front of the variable.**

**Step 4: Check your answer.**

**I find this is the quickest and
easiest way
to approach linear equations.**

** Example
1**: Solve the equation .

***Inverse of mult. by -3 is div.
by -3**

If you put 1 back in for x in the original problem you
will see that **1
is the solution we are looking for.**

***Get all x terms
on one side**

***Inverse of add. 3 is sub. 3**

***Inverse of mult. by -1 is div.
by -1**

If you put 9 back in for x in the original problem you
will see that** 9 is the solution we are looking for.**

***Get all the x terms on one side**

***Inverse of add. 2 is sub. 2**

***Inverse of mult. by -3 is div.
by -3**

If you put 4/3 back in for x in the original problem
you will see that **4/3
is the solution we are looking for.**

***Get all the y terms on one side**

***Inverse of sub. 20 is add 20**

***Inverse of mult. by 20 is div.
by 20**

If you put 3/2 back in for *y *in
the original
problem you will see that **3/2 is the solution we are looking for.**

A contradiction is an equation with one variable that has no solution.

***Get all the x terms on one side**

**Whenever your variable drops
out AND you end
up with a false statement, then after all of your hard work, there is
NO
SOLUTION.**

So, **the answer is no solution.**

An identity is an equation with one variable

that has
all numbers as
a solution.

***Get all the x terms on one side**

So, **the answer is all real numbers**.

** Practice Problems**

These are practice problems to help bring you to the
next level.
It will allow you to check and see if you have an understanding of
these
types of problems. **Math works just like
anything
else, if you want to get good at it, then you need to practice
it.
Even the best athletes and musicians had help along the way and lots of
practice, practice, practice, to get good at their sport or instrument.**
In fact there is no such thing as too much practice.

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 - 1d:Solve the given equation.

** Need Extra Help on these Topics?**

This webpage helps you with solving linear equations.

**Go to Get
Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for
some
more suggestions.**

Last revised on July 26, 2011 by Kim Seward.

All contents copyright (C) 2001 - 2010, WTAMU and Kim Seward. All rights reserved.