Question

How do you solve `(2y-3)/5+(9y-9)/4 = 21`?

Answer 1

Get a common denominator

`[4(2y-3)]/(4xx5)+[5(9y-9)]/[5xx4]=21`

`[8y-12]/20+[45y-45]/20=21`

`[53y-57]/20=21`

Multiply both sides by 20

53y-57=420

add 57

53y=477

divide by 53

y=9

Answer 2

`y=9`

Explanation:

Solve:

`(2y-3)/5+(9y-9)/4=21`

In order to add or subtract fractions, they must have the same denominator. The least common denominator (LCD) for `1,4,5` is `20`. If we multiply both sides of the equation by `20`, we can cancel the denominators.

`color(red)cancel(color(blue)(20))^4xx(2y-3)/color(red)cancel(color(black)(5))^1+color(red)cancel(color(blue)(20))^5xx(9y-9)/color(red)cancel(color(black)(4))^1=21xxcolor(blue)20`

Simplify.

`4(2y-3)+5(9y-9)=420`

Expand.

`8y-12+45y-45=420`

Simplify.

`53y-57=420`

Add `57` to both sides.

`53y=420+57`

Simplify.

`53y=477`

Divide both sides by `53`.

`y=477/53`

Reduce.

`y=9`