# How do you solve for y in (y+5)/ 2 - y/3 =1?

Jun 10, 2018

$y = - 9$

#### Explanation:

Solve:

$\frac{y + 5}{2} - \frac{y}{3} = 1$

The LCM of $2$ and $3$ is $6$. Multiply both sides by $6$.

$\frac{6 \left(y + 5\right)}{2} - \frac{6 \left(y\right)}{3} = 1 \left(6\right)$

Simplify.

$\frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}}^{3} \left(y + 5\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} ^ 1 - \frac{{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}}^{2} \left(y\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} ^ 1 = 1 \left(6\right)$

$3 \left(y + 5\right) - 2 y = 6$

Expand.

$3 y + 15 - 2 y = 6$

Subtract $15$ from both sides.

$3 y - 2 y = 6 - 15$

Simplify.

$y = - 9$

Jun 10, 2018

$y = - 9$

#### Explanation:

As we know, when subtracting any fraction, we must have like denominators. To achieve this, let's multiply the first one by $\frac{3}{3}$ and the second by $\frac{2}{2}$. We now have

$\textcolor{b l u e}{\left(\frac{3}{3}\right)} \frac{y + 5}{2} - \textcolor{b l u e}{\left(\frac{2}{2}\right)} \left(\frac{y}{3}\right) = 1$

Which simplifies to

$\frac{3 \left(y + 5\right) - 2 y}{6} = 1$

Distributing the $3$, we now have

$\frac{3 y + 15 - 2 y}{6} = 1$

Combining like terms in the numerator, we get

$\frac{y + 15}{6} = 1$

Multiply both sides by $6$ to get

$y + 15 = 6$

Lastly, subtracting $15$ from both sides gives us

$y = - 9$

Hope this helps!