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3.07 Literal Equations Basic Algebra: One Step at a Time, Page 293-296: #9, 10, plus 2 extra problems,12, 22, 25, 27, 31, 32, 33. Bittinger: p.101: 17, 21, 31, 37, 53. Dr. Robert J. Rapalje Seminole State College of Florida Sanford, FL 32773
To see Section 3.07, with explanations, examples, exercises, and answers, click here!
9. Solve for
x:
Solution: First, remove parentheses by the distributive property.
Next, get all the
Now, factor the common factor of x:
Finally, since the x has been multiplied by
NOTE: Don't be tempted to divide out the a or the c! These are "terms"! Never divide out TERMS--only FACTORS!!
10. Solve for
x:
Solution: First, remove parentheses by the distributive property.
Next, get all the
Now, factor the common factor of
Finally, since the x has been multiplied by
NOTE: Don't be tempted to divide out the a or the c! These are "terms"! Never divide out TERMS--only FACTORS!!
Extra Problem #1 (from Chris).
Solve for
x:
Solution: First, remove parentheses by the distributive property.
Next, get all the x terms on the left side by subtracting
Now, factor the common factor of x:
Finally, since the x has been multiplied by
Extra Problem #2
Solve for
x:
Solution: First, remove parentheses by the distributive property.
Next, get all the x
terms on the right side by adding
Now, factor the common factor of x:
Finally, since the x
has been multiplied by
12. Solve for
x:
Solution: First, remove parentheses by the distributive property.
Next, notice that there is only one
Finally, in order to solve for
you must divide both sides of the equation by
NOTE: Don't be tempted to divide out the
22.
Solution:
Since
you are solving for
25.
Solution:
Since there is a denominator of
Next, remember that you are solving for
27.
Solution:
Since there is a denominator of
Next, remember that you are solving for
28. Given
Solution:
Since there is a denominator of
Next,
remember that you are solving for
31. Given:
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
Now, undo
the multiplication by
The other
method involves multiplying both sides of the equation by the denominator
which is
Subtract
To solve
for
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:
32. Notice that this is the same problem as #11, but in reverse! Begin with:
Given:
Solution: Begin by “undoing” the fraction
Next,
“undo” the
In conclusion, notice that the problem for #11 is the answer for #12, and vice-versa.
33. Given 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!!
Bittinger Problems Page 101: #17, 21, 31, 37
17.
Solution:
Since you are solving for
This equation can be written
Next, divide both sides by
You can divide out the 2 factors on the left side, but NOT on the right
side, since the
21.
Solution:
Since there is a denominator of
Next, remember that you are solving for
31. Given:
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
Now, undo
the multiplication by
The other
method involves multiplying both sides of the equation by the denominator
which is
Subtract
To solve
for
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:
37.
Solution:
Since you are solving for
As you can see, the denominator divides out:
Next, remove the parentheses by the Distributive Property:
In order to solve for
Next, in order to isolate the
Finally, divide both
sides by
The
The final answer is By the way, several other forms of the answer are equally acceptable. For example, the three terms in the numerator can be arranged in ANY order!
53. Solve
for
c:
Solution:
First, get all the
Next, you have to get the
Finally, since the
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