**Quote:**

I didn't understand why we have to multiply both sides of the equation.

We do that to get rid of the denominators.

**Quote:**

What I did is finding LCD that is 6, and I did not multiply 4 by 6...

6 is the LCD of the first two fractions only. Knowing it you can add 1/3 and 1/2 .

1/2 + 1/3 = 3/6 + 2/6 = (3 + 2)/6 = 5/6

The original equation becomes:

5/6 + 1/

*x* = 4

There is still a way to go. There will be a multiplication of 4 by 6 somewhere along it.

**Quote:**

Also, I didn't understand what is 19/6 ?

We got the answer

*x* = 6/19 . If we want to check that we did no mistakes along the way and this answer is in fact the correct one, we can plug

*x* = 6/19 in the original equation.

1/3 + 1/2 + 1/(6/19)

?= 4

If this equality is true, then the solution

*x* = 6/19 is correct.

The third term, 1/(6/19) , equals 19/6 . This is where we get 19/6.

1/3 + 1/2 + 19/6 ?= 4

The remaining step is to sum the fractions and see if we get 4.