Question

How do you solve `\frac { 4} { 5x } = \frac { 3} { 2x - 1}`?

Answer 1

`x = -4/7`

Explanation:

First, to eliminate the fractions and to keep the equation balanced you need to multiply each side of the equation by the value of each of the denominators:

`((5x)(2x - 1)4)/(5x)=((5x)(2x - 1)3)/(2x-1)`

`(cancel((5x))(2x - 1)4)/cancel((5x))=((5x)cancel((2x - 1))3)/cancel((2x-1))`

`(2x - 1)4)=(5x)3`

Next, expand the terms within parenthesis:

`8x - 4 = 15x`

Now you can solve for `x` while keeping the equation balanced:

`8x - 8x - 4 = 15x - 8x`

`0 - 4 = (15 - 8)x`

`-4 = 7x`

`(-4)/7 = (7x)/7`

`-4/7 = (cancel(7)x)/cancel(7)`

`x = -4/7`