Question

How do you solve for n in `(1/2)x-(2/3)=4x`?

Answer 1

`x = -4/21`

Explanation:

Given
`(1/2)x−(2/3) = 4x`
Solve for `x`

1) Clear the first denominator by multiplying all the terms on both sides by 2 and letting the denominator cancel.
After you have multiplied and canceled, you will have this:
`x - (4/3) = 8x`

2) Clear the second fraction by multiplying all the terms on both sides by 3 and letting the denominator cancel.
After you have multiplied and canceled, you get this:
`3x - 4 = 24x`

3) Subtract `3x` from both sides to get all the `x` terms together
`- 4 = 21x`

4) Divide both sides by 21 to isolate `x`
`-4/21 = x` `larr` answer

Answer
`x = -4/21`
..................................

Check
Sub in `-4/21` in the place of `x` in the original equation

`(1/2)x−(2/3) = 4x`

`(1/2)(-4/21)−(2/3) = 4(-4/21)`

Cancel
`(1/(cancel2^1))(-cancel4^2/21)−(2/3) = 4(-4/21)`

Clear the parentheses by distributing the 4
`- 2/21- 2/3 = -16/21`

Rewrite with a common denominator
`- 2/21- 14/21 = -16/21`

Combine like terms
`- 16/21 = -16/21`
Check!