Game Development Reference
In-Depth Information
With the use of a number line, you distinguish the absolute value with respect to
the origin of the number line, which is zero. The absolute value of a number is its
distance from the origin.
Given such an understanding, when you solve an equation that involves an
absolute value, then you deal with two absolute distances. Consider this equation:
jx 2 5
Working with this problem involves two solutions. You arrive at these solutions
by anticipating that j x 2 j can be equal to either a positive or negative number.
The positive or negative number in this instance is 5 or 5. Given this situation,
your solution involves two equations:
x 2 ¼ 5
x 2 ¼ 5
x 2 þ 2 ¼ 5 þ 2
x 2 þ 2 ¼ 5 þ 2
x ¼ 7
x ¼ 3
To verify the correctness of these solutions, you substitute them back into the
original equation:
j 7 2 j¼j 5 5
j 3 2 j¼j 5 5
Here is a second example. It works the same way. You begin with an equation
that includes an expression that embodies an absolute value. You then solve the
equation for the two values the absolute value allows:
jx þ 7 8
You then proceed with solutions as follows:
x þ 7 ¼ 8
x þ 7 ¼ 8
x þ 7 7 ¼ 8 7
x þ 7 7 ¼ 8 7
x ¼ 1
x ¼ 15
As with the previous example, to test the correctness of these solutions, you
substitute them back into the original equation:
j 1 þ 7 j¼j 8 8
j 15 þ 7 j¼j 8 8
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