Question

How do you solve `\frac { 2} { 5x } + \frac { 7} { 4x } = - 3`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(20x)` to eliminate the fractions while keeping the equation balanced:

`color(red)(20x)(2/(5x) + 7/(4x)) = color(red)(20x) xx -3`

`(color(red)(20x) xx 2/(5x)) + (color(red)(20x) xx 7/(4x)) = -60x`

`(4color(red)(cancel(20)cancel(x)) xx 2/(color(red)(cancel(color(black)(5)))color(red)(cancel(color(black)(x))))) + (5color(red)(cancel(20)cancel(x)) xx 7/(color(red)(cancel(color(black)(4)))color(red)(cancel(color(black)(x))))) = -60x`

`(4 xx 2) + (5 xx 7) = -60x`

`8 + 35 = -60x`

`43 = -60x`

Now, divide each side of the equation by `color(red)(-60)` to solve for `x` while keeping the equation balanced:

`43/color(red)(-60) = (-60x)/color(red)(-60)`

`-43/60 = (color(red)(cancel(color(black)(-60)))x)/cancel(color(red)(-60))`

`-43/60 = x`

`x = -43/60`