How do you solve -\frac { 3} { 2} y - \frac { 9} { 7} = - \frac { 3} { 2}?

Mar 5, 2017

See the entire solution process below:

Explanation:

First, eliminate the fractions and keep the equation balanced by multiplying each side of the equation by $\textcolor{red}{14}$.

$\textcolor{red}{14} \left(- \frac{3}{2} y - \frac{9}{7}\right) = \textcolor{red}{14} \times - \frac{3}{2}$

$\left(\textcolor{red}{14} \times - \frac{3}{2} y\right) - \left(\textcolor{red}{14} \times \frac{9}{7}\right) = \cancel{\textcolor{red}{14}} 7 \times - \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}$

$\left(\cancel{\textcolor{red}{14}} 7 \times - \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} y\right) - \left(\cancel{\textcolor{red}{14}} 2 \times \frac{9}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}\right) = - 21$

$- 21 y - 18 = - 21$

Next, add $\textcolor{red}{18}$ to each side of the equation to isolate the $y$ term while keeping the equation balanced:

$- 21 y - 18 + \textcolor{red}{18} = - 21 + \textcolor{red}{18}$

$- 21 y - 0 = - 3$

$- 21 y = - 3$

Now, divide each side of the equation by $\textcolor{red}{- 21}$ to solve for $y$ while keeping the equation balanced:

$\frac{- 21 y}{\textcolor{red}{- 21}} = - \frac{3}{\textcolor{red}{- 21}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 21}}} y}{\cancel{\textcolor{red}{- 21}}} = \frac{1}{7}$

$y = \frac{1}{7}$