Game Development Reference
In-Depth Information
effective as a way of understanding how equations work. Working with an
equation is a process of balancing. When you relate numbers to each other using
an equation, you make it so that you can change the way you represent numbers.
As you change the way you represent the numbers, you can solve the equation for
specific values.
An equation, then, consists of a relation you establish between numbers. When
you establish the relation, you assert that a balance or condition exists between
the representations you provide of the numbers.
You balance equations by manipulating their terms. As the discussion in Chapter 2
emphasized, you manipulate the terms of an equation using the properties of ad-
dition, subtraction, multiplication, and division. When you manipulate the terms
and expressions of an equation, the goal of your activity is to preserve the equality
of the terms.
Addition and Subtraction
Solving equations using addition and subtraction provides what proves to be the
easiest approach to viewing how equations work. Here's an equation:
x þ
3
¼
7
This equation involves one unknown term (
x
). If you solve the equation, you find
the value of the unknown term. To find this value, you can subtract 3 from both
sides of the equation:
x þ
3
3
¼
7
3
x þ
0
¼
4
x ¼
4
As you carry out the operation, you preserve the equality. In the end, you
eliminate enough terms from the equation to find the lone value of
x
.
Subtraction constitutes a form of addition (adding the inverse). You can begin
with an equation of a slightly different form:
x
3
¼
7
x
3
þ
3
¼
7
þ
3
x ¼
10
