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SOLVING LINEAR EQUATIONS INVOLVING FRACTIONS
Jump right to the exercises!
The concepts for this exercise are summarized below.
For a complete discussion, read the text.
When solving equations involving fractions, it's usually easiest to clear fractions first
by multiplying by the least common denominator of all the fractions involved,
as illustrated in the examples below.
EXAMPLE:
Solve:
2
3
x
+
6
=
1
Solution:
Write a nice clean list of equivalent equations:
|
2
3
x
+
6
=
1
|
(original equation) |
| 3(2
3x+6
)=3(1)
|
(multiply both sides by 3 ) |
| 2x+18=
3 |
(simplify; all fractions are gone) |
| 2x=-15
|
(subtract 18 from both sides) |
| x=-15
2 |
(divide both sides by 2 ) |
EXAMPLE:
Solve:
-3x-
89=
56
Solution:
| -3x-
89=
56
|
(original equation) |
| 18(-3x
-89
)=18(
56)
|
(multiply both sides by 18 , which is the least common multiple of 9 and 6 ) |
| -54x-16
=15 |
(simplify) |
| -54x=31
|
(add 16 to both sides) |
| x=-31
54 |
(divide both sides by -54 ) |
Report your answers as integers, or as fractions in simplest form.
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.