Question

How do you solve `1/4(x-5)-1/5(2x+1)=1/2(3x-7)`?

Answer 1

`41/33 = x`

Explanation:

We could use the distributive law to get rid of the brackets, but it would be easier to get rid of the denominators altogether. Multiply each term by 20.

`color(red)(20xx)1/4(x-5)-color(red)(20xx)1/5(2x+1)=color(red)(20xx)1/2(3x-7)`

`cancel20^5xx1/cancel4(x-5)-cancel20^4xx1/cancel5(2x+1)=cancel20^10xx1/cancel2(3x-7)`

`5(x-5) -4(2x+1) = 10(3x-7)`

`5x-25 -8x-4 =30x-70`

`-25-4+70=30x-5x+8x`

`41=33x`

`41/33 = x`