Question

How do you solve `2/3 n = 4n - 10/3 n - 1/2`?

Answer 1

Solving the equation leads to `0 = -3`
This is false. `rArr` There is no solution.

Explanation:

The fractions are what make the equation look complicated.

Because it is an equation you can get rid of the fractions by multiplying each term by the LCM of the denominators.
(This is somewhat easier than trying to make all the denominators the same first.)
`2/3n = 4n- 10/3n - 1/2 " "` (LCM of 3 and 2 is `color(red)6)`

`color(red)6xx2/3n = color(red)6xx4n - color(red)6xx10/3n - color(red)6xx1/2`

Now cancel the denominators and simplify.

`color(red)cancel6^2xx2/cancel3n = color(red)6xx4n - color(red)cancel6^2xx10/cancel3n - color(red)cancel6^3xx1/cancel2`

`4n = 24n -20n -3`
`4n= 4n-3`
`0 = -3` `" "` This is obviously false.

There is no solution to this equation.