Rearranging Formulae with Multiple Terms
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Rearranging Formulae with Multiple Terms
To rearrange formulae with multiple terms on either side, we must try to simplify the equation as
much as possible.
1. If there is more than one term on the side of the equation that has the desired variable, you
have to perform the proper operation (addition or subtraction) to both sides to remove it.
** It is imperative that anything you do to the values on the right side of the equal sign is also
done to the values on the left side of the equal sign **
2. If there is only one term on the side of the equation that has the desired variable, you have to
perform the proper operation (multiplication or division) to both sides to remove it.
** It is imperative that anything you do to the values on the right side of the equal sign is also
done to the values on the left side of the equal sign **
Example 1: Solve the following equation:
We want to find x by itself. First we see how many terms are in the equation on the side with
the desired variable. There is only one term so we can skip to Step 2.
We want the variable by itself. There is only 1 term on both
sides of the equal sign so want to get rid of the denominator
(which in this case is “4”). To do this, we multiply both sides by
the denominator.
Now we simplify the expression.
x – 2 = 20
We now have the variable we want plus another term. To get
the variable by itself, we need to perform the appropriate
operation to cancel it out. (In this case, we will be adding it.)
Remember: whatever you do to one side, you MUST do to the
other.
x – 2 +2 = 20 +2
x = 22
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Rearranging Formulae with Multiple Terms
Example 2: Solve the following equation:
We want to find z by itself. First we see how many
terms are in the equation on the side with the desired
variable. There are two terms, so we want to get rid of
the one that does not contain the desired variable
On the right side, we have a fraction subtracted by an
integer. We can do the subtraction by first creating a
common denominator. In this case, 2 is a common
denominator.
Now that bother values are over a common
denominator, we can merge the two fractions and
perform the subtraction on the numerators.
We still want z by itself so we have to divide both sides
by 2 (from the numerator of the term containing the z)
( )
( )
*Note: dividing by an integer is the same as multiplying
by a fraction with the integer in the denominator
So we have but we want z. Since there is only 1 term
on the side with the variable, and the variable is in the
denominator, we multiply both sides by the
denominator.
Now that we have the variable as a numerator, we want
to get rid of the coefficient of
. To do this, we have
to multiply both sides by the denominator (4) and
divide both sides by the numerator (-13).
( )
( )(
)
Now we simplify.
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Rearranging Formulae with Multiple Terms
Example 3: Solve the following equation:
Looking at both sides of the equation we have two
terms on the side with the variable and one is a mixed
fraction. We want to first simplify the mixed fraction to
make it easier to work with. To do this, we set the
whole number as a fraction with the common
denominator of the fraction it is already with. From
there, we add the two numerators together.
We now have two terms on the side containing the
variable. We want to find the variable by itself so we
have to do the appropriate operation to remove the
other term from that side. In this case, we want to
subtract from both sides.
From here, we find a common denominator to simplify
the right side of the equation.
Now we want to get the variable in the numerator. To
do this, we have to multiply both sides by the
denominator of the term containing the variable.
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Rearranging Formulae with Multiple Terms
Now that we have the variable as a numerator, we
want to get rid of the coefficient of . To do this, we
have to multiply both sides by the denominator (2) and
divide both sides by the numerator (7).
( )
( )
or
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Rearranging Formulae with Multiple Terms
Try the following problems:
1. Solve the following equation:
2. Solve the following equation:
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Rearranging Formulae with Multiple Terms
3. Solve the following equation:
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Rearranging Formulae with Multiple Terms
4. Solve the following equation:
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Rearranging Formulae with Multiple Terms
5. Solve the following equation:
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