# How do you solve -5\frac { 2} { 3} - \frac { 3} { 4} b = - 4\frac { 5} { 12}?

Nov 4, 2017

$b = - 1 \frac{2}{3}$

#### Explanation:

color(blue)(-5 2/3-3/4 b=-4 5/12

First of all, simplify all of the mixed fractions (in the form of $x \frac{y}{z}$)

$\rightarrow - \frac{17}{3} - \frac{3}{4} b = - \frac{53}{12}$

$\rightarrow - \frac{3}{4} b = - \frac{53}{12} + \frac{17}{3}$

$\rightarrow - \frac{3}{4} b = \frac{- 53 + 68}{12}$

$\rightarrow - \frac{3}{4} b = \frac{15}{12}$

$\rightarrow b = {\cancel{15}}^{5} / {\cancel{12}}^{3} \times - {\cancel{4}}^{1} / {\cancel{3}}^{1}$

color(green)(rArrb=-5/3=-1 2/3

Hope that helps!!! ☺♠☻

Nov 4, 2017

$b = - 1 \left(\frac{2}{3}\right)$

#### Explanation:

Convert the individual terms to improper fractions.
$- \frac{17}{3} - \frac{3 b}{4} = - \frac{53}{12}$
Taking 12 as L C M for L H S,
$\frac{- 68 - 9 b}{\cancel{12}} = - \frac{53}{\cancel{12}}$
$- 9 b = 68 - 53$
$b = - \frac{15}{9} = - \frac{5}{3} = - 1 \left(\frac{2}{3}\right)$

Nov 4, 2017

$b = - \frac{5}{3}$

#### Explanation:

Change all the fractions to improper fractions first:

$- 5 \frac{2}{3} - \frac{3}{4} b = - 4 \frac{5}{12}$

$\frac{- 17}{3} - \frac{3 b}{4} = \frac{- 53}{12}$

To get rid of the fractions, multiply each term by the LCD of the denominators (which is $12$)

$\frac{- 17 \textcolor{b l u e}{\times 12}}{3} - \frac{3 b \textcolor{b l u e}{\times 12}}{4} = \frac{- 53 \textcolor{b l u e}{\times 12}}{12}$

Cancel the denominators and simplify

$\frac{- 17 \textcolor{b l u e}{\times {\cancel{12}}^{4}}}{\cancel{3}} - \frac{3 b \textcolor{b l u e}{\times {\cancel{12}}^{3}}}{\cancel{4}} = \frac{- 53 \textcolor{b l u e}{\times \cancel{12}}}{\cancel{12}}$

$- 68 - 9 b = - 53$

$- 68 + 53 = 9 b$

$\text{ } - 15 = 9 b$

$- \frac{15}{9} = b$

$b = - \frac{5}{3}$