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

2 Answers
May 10, 2018

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!

May 10, 2018

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