Environmental Engineering Reference
In-Depth Information
Note:
Step 1 expresses the whole equation, step 2 shows that 4 has been sub-
tracted from both sides of the equation, and in step 3 both members have been
divided by 6.
Note:
An equation is kept in balance (both sides of the equal sign are kept equal)
by subtracting the same number from both sides (members), adding the same
number to both, or dividing or multiplying both by the same number.
The expression 6
x
+ 4 = 19 is called a
conditional equation
because it is true
only when
x
has a certain value. The number to be found in a conditional equation
is called the
unknown number
, the
unknown quantity
, or, more briefly, the
unknown
.
Solving an equation requires finding the value or values of the unknown that
make the equation true. Keep in mind that the unknown is a variable that we are try-
ing to solve. The unknown variable is usually represented by a letter, such as
x
. When
solving for an unknown variable,
x
must be in the numerator or
x
must be by itself
on one side of the equation. If
x
is the denominator it can trade places with a number
on the other side of the = sign. Transpose or flip-flop the equation as shown below.
This is the only time you can move
x
. If
x
is in the numerator, DO NOT MOVE
x
.
■
Example 8.1
Problem:
3
=
6
x
Solution:
3
6
05
=
x
.
=
x
Let's take a look at another equation:
W
=
F
×
D
where
W
= Work.
F
= Force.
D
= Distance.
Thus,
Work = Force (lb) × Distance (ft or in.)
The resulting quantity is expressed in ft-lb or in.-lb.
Suppose we have this equation:
60 =
x
× 2
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