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

May 10, 2018

$b = - \frac{119}{286}$

#### Explanation:

$\left(4 + \frac{2}{3}\right) b + \frac{4}{5} = \left(2 + \frac{1}{7}\right) b - \frac{1}{5} b - \frac{1}{3}$

$\frac{14}{3} b + \frac{4}{5} = \frac{15}{7} b - \frac{1}{5} b - \frac{1}{3}$

$14 \cdot 35 b + 4 \cdot 21 = 15 \cdot 15 b - 21 b - 35$

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

$490 b - 204 b = - 35 - 84$

$286 b = - 119$

$b = - \frac{119}{286}$

May 10, 2018

$b = - \frac{119}{286}$

#### Explanation:

First change the mixed numbers to improper fractions:

$4 \frac{2}{3} b + \frac{4}{5} = 2 \frac{1}{7} b - \frac{1}{5} b - \frac{1}{3}$

$\frac{14 b}{3} + \frac{4}{5} = \frac{15 b}{7} - \frac{b}{5} - \frac{1}{3}$

You can get rid of the fractions by multiplying each term by the LCM of the denominators, which is $3 \times 5 \times 7 = 105$

$\frac{\textcolor{b l u e}{{\cancel{105}}^{35} \times} 14 b}{\cancel{3}} + \frac{\textcolor{b l u e}{{\cancel{105}}^{21} \times} 4}{\cancel{5}} = \frac{\textcolor{b l u e}{{\cancel{105}}^{15} \times} 15 b}{\cancel{7}} - \frac{\textcolor{b l u e}{{\cancel{105}}^{21} \times} b}{\cancel{5}} - \frac{\textcolor{b l u e}{{\cancel{105}}^{35} \times} 1}{\cancel{3}}$

This leaves us with an equation without fractions,

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

$490 b + 84 = 204 b - 35$

$490 b - 204 b = - 35 - 84$

$286 b = - 119$

$b = - \frac{119}{286}$