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

Nov 20, 2017

$x = - \frac{4}{21}$

#### 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:
$x - \left(\frac{4}{3}\right) = 8 x$

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:
$3 x - 4 = 24 x$

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

4) Divide both sides by 21 to isolate $x$
$- \frac{4}{21} = x$ $\leftarrow$ answer

$x = - \frac{4}{21}$
..................................

Check
Sub in $- \frac{4}{21}$ 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
$- \frac{2}{21} - \frac{2}{3} = - \frac{16}{21}$

Rewrite with a common denominator
$- \frac{2}{21} - \frac{14}{21} = - \frac{16}{21}$

Combine like terms
$- \frac{16}{21} = - \frac{16}{21}$
Check!