Solving Linear Equations Containing Fractions
Solve:
Solution
First, find the LCD of the fractions.
Step 1 Factor each denominator
into its prime factors.
Step 2 List each factor the greatest
number of times that it appears
in any one of the denominators.
Step 3 Multiply the prime factors in the list.
So, the LCD of the fractions is 40. |
8 = 2 · 2
·2 20 =
2 · 2
· 5
10 = 2 · 5
2, 2, 2, 5
2 · 2
· 2 · 5 =
40 |
Next, clear the fractions:
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• Multiply each side by the LCD, 40. |
|
• Simplify.
|
5x = 2x - 4 |
Then, solve the equation for x:
• Subtract 2x from both sides. |
3x = -4 |
• Divide both sides by 3.
We leave the check to you.
The solution is
. |
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Note:
can also be written as
|