Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

APPENDIX A | Basic Mathematics Review 637
A.4 Basic Algebra: Solving Equations
An equation is a mathematical statement that indicates two quantities are identical. For
example,
12 5 8 1 4
Often an equation will contain an unknown (or variable) quantity that is identified with
a letter or symbol, rather than a number. For example,
12 5 8 1 X
In this event, your task is to find the value of X that makes the equation “true,” or balanced.
For this example, an X value of 4 will make a true equation. Finding the value of X
is usually called solving the equation.
To solve an equation, there are two points to keep in mind
1. Your goal is to have the unknown value (X) isolated on one side of the equation.
This means that you need to remove all of the other numbers and symbols that
appear on the same side of the equation as the X.
2. The equation remains balanced, provided you treat both sides exactly the same. For
example, you could add 10 points to both sides, and the solution (the X value) for
the equation would be unchanged.
■ Finding the Solution for an Equation
We will consider four basic types of equations and the operations needed to solve them.
1. When X Has a Value Added to It An example of this type of equation is
X 1 3 5 7
Your goal is to isolate X on one side of the equation. Thus, you must remove the 13 on
the left-hand side. The solution is obtained by subtracting 3 from both sides of the equation:
X 1 3 2 3 5 7 2 3
X 5 4
The solution is X 5 4. You should always check your solution by returning to the original
equation and replacing X with the value you obtained for the solution. For this example,
X 1 3 5 7
4 1 3 5 7
7 5 7
2. When X Has a Value Subtracted From It An example of this type of equation is
X 2 8 5 12
In this example, you must remove the 28 from the left-hand side. Thus, the
solution is obtained by adding 8 to both sides of the equation:
X 2 8 1 8 5 12 1 8
X 5 20