Game Development Reference
In-Depth Information
remain the same if you extend them through addition:
a þ c
>
b þ c
and
a þ c b þ c
Given that you can extend these relations to include the addition of additive
inverses, you can safely add or subtract values to remove or isolate values on both
sides of the inequality without changing the relation.
Here is an equation that involves inequalities and addition:
x þ
4
6
x þ
4
4
<
<
6
4
Undoing the addition of 4
:
x
<
2
You can represent this inequality by graphing it on a number line. The filled
circle indicates that valid solutions are any numbers less than 2. In other words,
2 and any number greater than 2 are not members of the solution set.
As with equations involving relations of equality, you can substitute your
solution into the original equation to test its validity. In this instance, the
solution consists of a range of numbers less than 2, which you can designate as
x jx
2. This expression reads that the solution is any number
x
such that
x
is
less than 2. Using this expression as a guide, you can arbitrarily designate the
following set:
<
f
2, 0, 1, 1
:
5
g
Given this set, you can substitute the solutions into the original equation:
ð
2
Þþ
4
<
6
¼
2
<
6
ð
1
:
5
Þþ
4
<
6
¼
5
:
5
<
6
ð
0
Þþ
4
<
6
¼
4
<
6
ð
1
Þþ
4
<
6
¼
5
<
6
In each instance, the expression proves true, verifying the validity of your
solution set.
