Question

How do you solve `6/5=2/(5n)`?

Answer 1

`6/5 = 2/"5n" : n = 1/3` (Decimal = 0.33333333333333333333............)

Explanation:

`6/5 * x/x = 2/"5n"`
Solve for `x`
`x = 2/6 = 0.33333333333333333......, 1/3`

`6/5 * 0.3333333/0.33333333 = 2/"5n"`

`5 * 0.333333333333333333..................... = 5n`

This means n = 0.3333333333333333333333......, `1/3`

Answer 2

`n=1/3`

Explanation:

Multiply both sides of the equation by the `color(blue)"lowest common multiple"` (LCM) of the denominators 5 and 5n

the LCM of 5 and 5n is 5n

`cancel(5)^1 n xx6/cancel(5)^1=cancel(5n)xx2/cancel(5n)`

`rArr6n=2`

To solve for n, divide both sides by 6

`(cancel(6) n)/cancel(6)=2/6`

`rArrn=2/6=1/3`

`color(blue)"As a check"`

Substitute this value into the right side and if it equals the left side then it is the solution.

`"right side "=2/(5xx1/3)=2/(5/3)==2/1xx3/5=6/5`

`rArrn=1/3" is the solution"`