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 Â· 2
Â·2 20 =
2 Â· 2
Â· 5
10 = 2 Â· 5
2, 2, 2, 5
2 Â· 2
Â· 2 Â· 5 =
40 
Next, clear the fractions:


â€¢ Multiply each side by the LCD, 40. 

â€¢ Simplify.

5x = 2x  4 
Then, solve the equation for x:
â€¢ Subtract 2x from both sides. 
3x = 4 
â€¢ Divide both sides by 3.
We leave the check to you.
The solution is
. 

Note:
can also be written as
