SOLUTION: Homework problem : x/2 + x/5 = 5/4 I solved the problem by finding the LCD = 20 20(x/2) + 20(x/5) = 20(5/4) Next I did the multiplication which came out to 10x + 4x = 25 Th

Algebra ->  Equations -> SOLUTION: Homework problem : x/2 + x/5 = 5/4 I solved the problem by finding the LCD = 20 20(x/2) + 20(x/5) = 20(5/4) Next I did the multiplication which came out to 10x + 4x = 25 Th      Log On


   



Question 335232: Homework problem :
x/2 + x/5 = 5/4
I solved the problem by finding the LCD = 20
20(x/2) + 20(x/5) = 20(5/4)
Next I did the multiplication which came out to
10x + 4x = 25
Then I added on the right side
14x = 25
And finally I divided
14x/14 = 25/14
x = 25/14
Is this right? and how do I check it? The plugging in the number for x is what I'm having trouble with, because I know you can't do (25/14)/2. I need to get the same answer on both sides of the equal sign (ex. y = y)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to check your answer when your answer is a fraction, and
there are fractions in the original problem:

x%2F2%22%22%2B%22%22x%2F5%22%22=%22%225%2F4

Write the fractions involving the variable as divisions:

%22x%F72%22%22%22%2B%22%22%22x%F75%22%22%22=%22%225%2F4

Then write them as multiplications by the reciprocals
("inverting the second then multiplying")

%22x%22%22%22%2A%22%221%2F2%22%22%22%22%22%22%2B%22%22%22%22%22%22%0D%0A%22x%22%22%22%2A%22%221%2F5%22%22%22%22%22%22=%22%22%22%225%2F4
Now you can substitute your fraction answer:

25%2F14%22%22%2A%22%221%2F2%22%22%22%22%22%22%2B%22%22%22%22%22%22%0D%0A25%2F14%22%22%2A%22%221%2F5%22%22%22%22%22%22=%22%22%22%225%2F4

       5
25%2F28%22%22%22%22%22%22%2B%22%22%22%22%22%22cross%2825%29%2F14%22%22%2A%22%221%2Fcross%285%29%22%22%22%22%22%22=%22%22%22%225%2F4

25%2F28%22%22%22%22%22%22%2B%22%22%22%22%22%22%0D%0A5%2F14%22%22%22%22%22%22=%22%22%22%225%2F4

25%2F28%22%22%22%22%22%22%2B%22%22%22%22%22%22%0D%0A5%2F14%22%22%2A%22%222%2F2%22%22%22%22=%22%22%22%225%2F4

25%2F28%22%22%22%22%22%22%2B%22%22%22%22%22%22%0D%0A10%2F28%22%22%22%22=%22%22%22%225%2F4

35%2F28%22%22%22%22=%22%22%22%225%2F4

Reduce the fraction on the left:

5%2F4%22%22%22%22=%22%22%22%225%2F4

But the easiest way to check is to convert your answer to a decimal using a
calculator, then store it in the memory of your calculator, then type the left
side into your calculator recalling the value you stored for x, and see if
you get the same decimal answer on both sides.
 
Edwin