# Question d3486

Jul 20, 2016

$\textcolor{b r o w n}{y = - \frac{54}{22}}$

#### Explanation:

Assumption: The equation is meant to be
$\frac{2}{3} y - \left(- 3 - \frac{y}{18}\right) = - \frac{y}{2}$

First dealing with the bracket. The minus outside the bracket is basically instructing that everything inside the bracket is multiplied by -1 giving.

$\textcolor{b r o w n}{\frac{2}{3} y + 3 + \frac{y}{18} \text{ "=" } - \frac{y}{2}}$

Subtract $\textcolor{b l u e}{3}$ from both sides

$\textcolor{b r o w n}{\frac{2}{3} y + \frac{y}{18} + 3 \textcolor{b l u e}{- 3} \text{ "=" } - \frac{y}{2} \textcolor{b l u e}{- 3}}$

$\textcolor{b r o w n}{\frac{2}{3} y + \frac{y}{18} \text{ "=" } - \frac{y}{2} - 3}$

Add $\textcolor{b l u e}{\frac{y}{2}}$ to both sides

$\textcolor{b r o w n}{\frac{2}{3} y + \frac{y}{18} \textcolor{b l u e}{+ \frac{y}{2}} \text{ "=" } \textcolor{b l u e}{\frac{y}{2}} - \frac{y}{2} - 3}$

color(brown)((2y)/3+y/18+y/2" "=" "-3#

Write over a common denominator

$\textcolor{b r o w n}{\frac{12 y + y + 9 y}{18} \text{ "=" } - 3}$

Multiply both sides by 18

$\textcolor{b r o w n}{22 y = - 54}$

Divide both sides by 22

$\textcolor{b r o w n}{y = - \frac{54}{22}}$