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14 Part I: Technical Mathematics
Always perform a check of your work by putting the value of the variable into the
original equation:
Part I.B
x + 3=
5
2+ 3=
5
Solving Equations Using Two or More Inverse Operations
To solve a problem such as ax + b = c, we must do a series of inverse operations on
both sides of the equation in order to isolate the variable a. In the following example,
addition and division inverse operations are employed in succession to find
the solution:
6a
2 = 22
6a
2+ 2 = 22+
2
6a
= 24
6a
÷ 6= 24÷
6
a = 4
Next, check the solution:
Solving Equations by Collecting Terms
6a 2 = 22
6× 4 2 = 22
24 2 = 22
22 = 22
To solve a problem where the variable and/or constants appear in more than two
terms, we must first collect terms, and then perform the inverse operations. For
example, to solve the equation 8z + 5 + 4z + –1 = 16, we must collect the variable
and the constant terms before proceeding with the solution:
8z+ 5+ 4z 1=
16
12z
+ 4 = 16
12z
+ 4 4 = 16
4
12z
= 12
12z
÷ 12 = 12÷
12
z = 1