Question

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

Answer 1

`b=-119/286`

Explanation:

`(4+2/3)b+4/5=(2+1/7)b-1/5b-1/3`

`14/3b+4/5=15/7b-1/5b-1/3`

`14*35b+4*21=15*15b-21b-35`

`490b+84=225b-21b-35`

`490b-204b=-35-84`

`286b=-119`

`b=-119/286`

\0/ here's our answer!

Answer 2

`b = -119/286`

Explanation:

First change the mixed numbers to improper fractions:

`4 2/3b +4/5 = 2 1/7b -1/5b -1/3`

`(14b)/3 +4/5 = (15b)/7 -b/5 -1/3`

You can get rid of the fractions by multiplying each term by the LCM of the denominators, which is `3xx5xx7 = 105`

`(color(blue)(cancel105^35xx)14b)/cancel3 +(color(blue)(cancel105^21xx)4)/cancel5 = (color(blue)(cancel105^15xx)15b)/cancel7 -(color(blue)(cancel105^21xx)b)/cancel5 -(color(blue)(cancel105^35xx)1)/cancel3`

This leaves us with an equation without fractions,

`490b +84 = 225b-21b-35`

`490b +84 = 204b-35`

`490b-204b = -35-84`

`286b = -119`

`b = -119/286`