Can someone explain how to do this (math)?

Question

I'm having trouble with this type of math, but before you read the rest, I DON'T JUST WANT AN ANSWER!!!
I want someone to explain every step of how to do this.
Also, please explain why you do something

Find the variable:

3n-2
------
5

equals

7
----
10

those are fractions by the way

Answer 1

it's a proportion, cross multiply to solve.

(3n - 2) x 10 = 5 x 7
30n - 20 = 35; add 20
30n = 55; divide by 30
n = 1 5/6

Answer 2

(3n -2)/5 = 7/10
or 10(3n -2) = 5 x 7 (Multiply denominatior from one side of the equation with the numerator of the other side)
or 30n - 20 = 35 (expand the equation by multiplying the factors)
or 30n = 35 + 20 (move variable and numbers on different side of the equations)
or 30n = 55 (reduce the equation)
or n = 55/30 (get the value of n by dividing the number of by the factor of n)
or n = 11/6

Answer 3

Equation:
(3n-2)/5 = 7/10

multiply both sides by 5 to get
5*{(3n-2)/5} = 5 *{7/10}
(3n-2) = 35/10
3n = 35/10 +2
3n = 35/10 +20/10 = 55/10 = 5.5
3n = 5.5 ~~~> n = 5.5/3

Answer 4

3n-2 7
------ = ----- cross multiply the denominator 30n-20 = 35
5 10

30n-20 = 35 = 6n - 4 = 7 (divided all terms by 5 )

6n - 4 + 4 = 7 + 4
6n = 11
6n/6 = 11 / 6
n = 1 5/6

Answer 5

(3n-2) / 5 = 7/10
3n-2 = (7 / 10 ) x 5
3n- 2 = 35 / 10
3n-2 = 3.5
3n = 3.5 +2
3n =5.5
n =5.5 / 3
n =1.8333 OR 1 5/6