SOLUTION: {{{3/4x+2/5= 1}}} I tried common denominators to get: 12x/20x + 8x/20x = 20x 20x/20x=20x ?

Algebra ->  Expressions-with-variables -> SOLUTION: {{{3/4x+2/5= 1}}} I tried common denominators to get: 12x/20x + 8x/20x = 20x 20x/20x=20x ?      Log On


   



Question 81187: 3%2F4x%2B2%2F5=+1
I tried common denominators to get:
12x/20x + 8x/20x = 20x
20x/20x=20x ?

Found 2 solutions by tutor_paul, Edwin McCravy:
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
3%2F4x%2B2%2F5=1
Remember back when you had to add fractions and find the LCD. The worse case was always to multiply the 2 denominators to find a common denominsator. Use that same thinking here. In this case, the LCD is 20x. Rewriting the problem in terms of the LCD, you get:
%2815%2B8x%29%2F20x=1
Solve for x:
15%2B8x=20x
12x=15
highlight%28x=5%2F4%29
Good Luck,
tutor_paul@yahoo.com

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Paul did it one way, but I think the most efficient way
is to clear of fractions:

3%2F%284x%29 + 2%2F5 = 1

Write the 1 as 1/1

3%2F%284x%29 + 2%2F5 = 1%2F1

Multiply every term by %28LCD%29%2F1 which is %2820x%29%2F1

Write %2820x%29%2F1· in front of every term: 

%2820x%29%2F1·3%2F%284x%29 + %2820x%29%2F1·2%2F5 = %2820x%29%2F1·1%2F1

In the first term cancel the 4x into the 20x and get 5.
In the second term, cancel the 5 into the 20 and get 4:

5%2F1·3%2F1 + %284x%29%2F1·2%2F1 = %2820x%29%2F1·1%2F1 

or

15%2F1 + %288x%29%2F1 = %2820x%29%2F1

 Erase the 1's on the bottoms:

15 + 8x = 20x

Subtract 8x from both sides, getting 15 on the left
and 12x on the right

          15 = 12x

Divide both sides by 12

           15%2F12 = %2812x%29%2F12

Reduce fraction:

             5%2F4 = x

Edwin