Note:
If you would like an in-depth review of fractions, click on Fractions.
Problem 5.3c:
Answer:
-0.197677
Solution:
Recall that you cannot divide by zero. Therefore, the first fraction is
valid if ,
and the third
fraction is valid is
If
or
turn
out to be the solutions, you must discard them as extraneous
solutions.
Multiply both sides by the least common multiple
(the smallest number that all
the denominators will divide into evenly). This step will eliminate all the
denominators.
which is equivalent to
which can be rewritten as
which can be rewritten as
which can be simplified to
All the work up to this point is translating the original equation,
, into an equation that is
easier to solve. The translated equation,
30x2-763x-152=0, can be
solved using the quadratic formula.
Solve for x using the quadratic formula
The exacts answers are
and the
approximate answers are 25.631011 and
Check the solution
by
substituting 25.631011 in the original equation for x. If the left side of
the equation equals the right side of the equation after the substitution,
you have found the correct answer.
Check the solution
by substituting -0.197677 in the original equation for x. If the left side of the equation
equals the right side of the equation after the substitution, you have found
the correct answer.
Since the left side of the equation almost equals the right side of the
equation after the substitution, we have verified that
-0.197677 is a solution. The reason the
check is not exact is because we rounded the answer.
You can also check your answer by graphing
(formed by subtracting the right side of the original equation from the left
side). Look to see where the graph crosses the x-axis; that will be the real
solution. Note that the graph crosses the x-axis at two places:
and -0.197677.
This verifies our
solution graphically.
We have verified our solution both algebraically and graphically.
If you would like to go back to the equation table of contents, click on
Contents