I still need a clear answer on this problem?

Question

Hi all, I asked this ? earlier today. I cannot solve it

1/x=1/5+1/20+1/15

If anyone could help me work it out and understand how you got the answer I would be very appreciative.

Answer 1

You first want to combine on the right side  (1/5+1/20+1/15) to do this you need to find a common denominator. Everything can be reduced to ?/5

Once you have that you wil need to get x by its self (multiplying it on both sides). and subtracting the first number you got from both sided.

Answer 2

Find the least common denominator of 5, 20 and 15, which is 60.

5 goes into sixty, 12 times, so 1/5 = 12/60.

20 goes into sixty, 3 times, so 1/20 = 3/60.

5 goes into sixty, 4 times, so 1/15 = 4/60.

Now that you have a common denominator, add the numerators.

(12 + 3 + 4) / 60 = 19/60.

Now you have:

1/x = 19/60

Multiply both sides by x/1

(x/1)*(1/x) = (x/1)*(19/60) ← [Hint: (x/1)*(1/x) reduces to 1 ]

1 = 19x/60

Multiply both sides by 60

60 * 1 = 60*(19x/60)

60 = 19x

19x = 60

Now, solve for x:

19x = 60

x = 60/19 or 3.2578947368

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Always check your work!

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Substitute 60/19 for x in the original equation:

1/x = 1/5 + 1/20 + 1/15

1/(60/19) = 1/5 + 1/20 + 1/15 ← [Hint: 1/(60/19) = 19/60]

19/60 = 1/5 + 1/20 + 1/15

Convert all denominators to 60:

19/60 = 12/60 + 3/60 + 4/60

19/60 = 19/60 ← Checks!

Good luck in your studies,

~ Mitch ~

EDIT: Sorry about my first answer - I misread the question... my bad.

P.S. - You're welcome to e-mail me if you have any questions.

Also, I apologize if my answer isn't clear.

(Equations don't type up very well).

Answer 3

Original equation:  1/x=1/5+1/20+1/15

First, you add 1/5+1/20+1/15.  You use the LCD, which is 60.

So it's 12/60+3/60+4/60=19/60.

You write the equation again, 1/x=19/60.

You multiply both sides by x to get rid of the fraction, 1/x.

Then you end up with 1=19/60x.  

You multiply 1=19/60x by 60 to isolate x.

Then you end up with 60=19x.

You divide both sides by 19 to isolate the x.

You end up with 60/19=x or x=60/19.

If you want an improper fraction, it is 3 3/19.