Question

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

Answer 1

`x = 110/124`

`x = 55/62` in simplest form

Explanation:

Solve for `@x` while keeping the equation balanced:

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

`(3/5)x + (5/2)x = 2 + 3/4`

`(2/2)(3/5)x + (5/5)(5/2)x = (4/4)2 + 3/4`

`(6/10)x + (25/10)x = 8/4 + 3/4`

`(31x)/10 = 11/4`

`(10/31)(31/10)x = (10/31)(11/4)`

`x = 110/124`

Answer 2

`x = 55/62`

Explanation:

In an equation with fractions you can get rid of the fractions by multiplying each term by the LCM of the denominators.

`3/5x-3/4 = -5/2x+2" "larr LCD = 20`

`(color(red)(20xx)3)/5x-(color(red)(20xx)3)/4 = -(color(red)(20xx)5)/2x+color(red)(20/1xx)2/1" "larr color(red)(xx20)`

`(color(red)(cancel20^4xx)3)/cancel5x-(color(red)(cancel20^5xx)3)/cancel4 = -(color(red)(cancel20^10xx)5)/cancel2x+color(red)(20/1xx)2/1`

`12x -15 = -50x +40`

`12x+50x = 40+15`

`62x = 55`

`x = 55/62`