Beginning and Intermediate Algebra - Wallace Math Courses ...

1.4
Solving Linear Equations - Fractions
Objective: Solve linear equations with rational coefficients by multiplying
by the least common denominator to clear the fractions.
Often when solving linear equations we will need to work with an equation with
fraction coefficients. We can solve these problems as we have in the past. This is
demonstrated in our next example.
Example 69.
3 7 5
x − =
4 2 6
+ 7
2
+ 7
2
Focus on subtraction
7
Add to both sides
2
Notice we will need to get a common denominator to add 5 7
+
6 2
common denominator of 6. So we build up the denominator, 7
�
3
2 3
can now add the fractions:
3 21 5
x − =
4 6 6
+ 21
6
+ 21
6
3 26
x =
4 6
3 13
x =
4 3
We can get rid of 3
4
Same problem, with common denominator6
Add 21
6
Reduce 26
6
to both sides
to 13
3
Focus on multiplication by 3
4
. Notice we have a
�
= 21
, and we
6
3
by dividing both sides by . Dividing by a fraction is the
4
same as multiplying by the reciprocal, so we will multiply both sides by 4
3 .
� 4
3
� 3
4
� �
13 4
x =
3 3
x = 52
9
Multiply by reciprocal
Our solution!
While this process does help us arrive at the correct solution, the fractions can
make the process quite difficult. This is why we have an alternate method for
dealing with fractions - clearing fractions. Clearing fractions is nice as it gets rid
of the fractions for the majority of the problem. We can easily clear the fractions
43