Question

How do you solve `\frac { 6} { 7x } = \frac { 4} { 5x - 1}`?

Answer 1

Multiply the fractions on each side of the equation by the same factor, which is the product of the denominators (`7x(5x - 1)`), to clear the fractions and keep the equation balanced:

`(7x(5x - 1) * 6)/(7x) = (7x(5x - 1)*4)/(5x - 1)`

`(cancel(7x)(5x - 1) * 6)/(cancel(7x)) = (7xcancel((5x - 1))*4)/cancel((5x - 1))`

`(5x -1)*6 = 7x*4`

We can now solve for `x` using the necessary mathematics while keeping the equation balanced:

`30x - 6 = 28x`

`30x - 28x - 6 + 6 = 28x - 28x + 6`

`2x = 6`

`(2x)/2 = 6/2`

`x = 3`