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1.08 Literal
Equations
College
Algebra: One Step at a Time. Page
134 -137: #8, 11, 12, 15, 17, 19
NEW
PROBLEMS: #15, 17
Dr. Robert J. Rapalje
Seminole Community College
Sanford, FL 32773
8. Given
 ,
solve for
 .
Solution:
Since there is a denominator of
 ,
multiply both sides by to
clear the fraction!
Next,
remember that you are solving for
,
and the  has
been multiplied by  and
 .
In order to “undo” the multiplication, you must divide both sides by
and
:
In order
to “undo” the square, you must take the square root of both sides:
There is
no need for a  in
this case, since is
a radius, and it cannot be negative.
11. Given:
 , solve for C.
Solution:
There are
at least two ways to solve for C in this problem. Both are equally correct,
but one is much easier that the other. The easy way to solve this is to
notice that the C has had two operations performed on it. First, C is
multiplied by the fraction  , and then  was added. To solve for C, you must UNDO these two
operations in reverse order. So, first undo the
 , by subtracting
from each side:
Now, undo
the multiplication by by multiplying both sides of the equation by the
reciprocal of which is  :
The other
method involves multiplying both sides of the equation by the denominator
which is  :
Subtract
 from each side:
To solve
for  just divide both sides by
 :
This is a
slightly different form of the answer obtained in the first method, if you
factor out the 5, the answer will be the same as above:
 .
12.
Notice that this is the same problem as #11, but in reverse! Begin
with:
Given:  , solve for F.
Solution: Begin by “undoing” the fraction
by multiplying both
sides of the equation by
Next,
“undo” the  by adding a to each side of the equation.
In conclusion, notice that the problem for #11 is the answer for #12, and
vice-versa.
15.  ,
solve for
 .
There are two ways to begin this problem, both of which result in
the same first step. You might want to “undo” the fraction by multiplying
both sides of the equation by
 ,
which looks like this:
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ALTERNATE METHOD OF ELIMINATING THE FRACTION |
|
The
other way to eliminate the fraction is to write it as a fraction equal
to a fraction and “cross-multiply.”
 |
The result is EXACTLY
the same:
Now, to solve for
,
you must get all the
terms
on one side, and the “non-”
terms on the other side. To do this subtract
 from
each side.
The last step is to divide both sides by
 ,
The on
the left side divides out, but the
on
the right side does NOT divide out! Why??? (See answer below!)
ANSWER: (Because they are FACTORS
on the left side, but
TERMS on the right
side!!)
17.
[Notice
the similarity between this exercise and #15. At first it looks like
exactly the same problem. The difference is that in #15 you were solving
for ,
whereas in #17 you are solving for
 .
The problems begin the same, but they are NOT the same!
]
,
solve for
.
There are two ways to begin this problem, both of which result in
the same first step. You might want to “undo” the fraction by multiplying
both sides of the equation by
,
which looks like this:
|
ALTERNATE METHOD OF ELIMINATING THE FRACTION |
|
The
other way to eliminate the fraction is to write it as a fraction equal
to a fraction and “cross-multiply.”
|
The result is EXACTLY
the same:
Now, to solve for
,
you must get all the
terms
on one side, and the “non-”
terms on the other side. To do this subtract
from
each side, exactly as in #15.
Now, to solve for
,
you must factor the common factor of
,
so as to get the in
one place.
Divide out the factors of  .
19. Given 
, solve for S.
First,
find the LCD,
which is FSU (to
all the
Florida
Gator
and Miami
Hurricane
fans,
GO
FLORIDA
STATE! )
In the first position, the F
divides out, leaving SU.
In the second position the S
divides out, leaving UF.
In the third position, the U
divides out, leaving FS.
Now,
in order to solve for S,
you have to get all the S
terms on one side of the equation. You can do that by
subtracting FS
from each side of the equation.
Now,
to solve for S,
you have to factor out the S
on the left side of the equation:
and divide
both sides by  :
IMPORTANT NOTE:
This problem is very much
like my own career, in that I started (and graduated!) at
FSU and
then ended up (and graduated also!) at UF—except
that I did NOT change
colors!!
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