Question

okay so I have an issue, I have to explain why I did a problem the way that I did, and I dont know how to explan it...

1/x+1/3=1/2
step 1: multiple everything by x

how do I explain the reasoning?

Answer 1

1/x = 1/2-1/3 subtracting to both sides 1/3
1/x = (3-2)/6 Find the common denominator, in this case 6
1/x = 1/6 multiply for 6x to both sides
6 = x

Answer 2

Thank you corec, but that is not what I was asking, I already have the problem with the answer, the question is why do I multiply everything by x as the first step...

this is the way that I worked the problem, how do I explain this to someone else?

1/x+1/3=1/2

1) multiply everything by x
x(1/x+1/3)=1/2(x)
1+x/3=x/2

2) multiply everything by 3
3(1+x/3)=(x/2)3
3+x-3x/2

3) multiply everything by 2
2(3+x)=2(3x/2)
6+2x=3x

4) subtract everything by 2x
6+2x-2x=3x-2x
6=x

This gives an answer x=6

Answer 3

you can say that your have to multiply everything by x to have x in the numerator. And you do the steps 2 and 3 to eliminates de denominator so we can have everything in the numerator like you see in the step 4. where you just have to subtract 2x to both sides to get the answer of x which is equal to 6. I hope this help!