# How do you solve 6/10=(p-7)/(p+10)?

Mar 25, 2018

The solution is $p = \frac{65}{2}$.

#### Explanation:

First, reduce the fraction:

$\frac{6}{10} = \frac{p - 7}{p + 10}$

${\textcolor{R e d}{\cancel{\textcolor{B l a c k}{6}}}}^{3} / {\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}^{5} = \frac{p - 7}{p + 10}$

$\frac{3}{5} = \frac{p - 7}{p + 10}$

$3 \left(p + 10\right) = 5 \left(p - 7\right)$

Use the distributive property:

$3 \cdot p + 3 \cdot 10 = 5 \cdot p - 5 \cdot 7$

$3 p + 30 = 5 p - 35$

$3 p + 30 \textcolor{b l u e}{+} \textcolor{b l u e}{35} = 5 p - 35 \textcolor{b l u e}{+} \textcolor{b l u e}{35}$

$3 p + 30 \textcolor{b l u e}{+} \textcolor{b l u e}{35} = 5 p \textcolor{red}{\cancel{\textcolor{b l a c k}{\textcolor{b l a c k}{-} 35 \textcolor{b l u e}{+} \textcolor{b l u e}{35}}}}$

$3 p + 30 \textcolor{b l u e}{+} \textcolor{b l u e}{35} = 5 p$

$3 p + 65 = 5 p$

$3 p + 65 \textcolor{b l u e}{-} \textcolor{b l u e}{3 p} = 5 p \textcolor{b l u e}{-} \textcolor{b l u e}{3 p}$

$\textcolor{red}{\cancel{\textcolor{b l a c k}{3 p}}} + 65 \textcolor{red}{\cancel{\textcolor{b l u e}{\textcolor{b l u e}{-} \textcolor{b l u e}{3 p}}}} = 5 p \textcolor{b l u e}{-} \textcolor{b l u e}{3 p}$

$65 = 5 p \textcolor{b l u e}{-} \textcolor{b l u e}{3 p}$

$65 = 2 p$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{65}}{2}} = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{2 p}}{2}}$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{65}}{2}} = \textcolor{b l u e}{\frac{\textcolor{b l a c k}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} p}}{\textcolor{red}{\cancel{\textcolor{b l u e}{2}}}}}$

$\textcolor{b l u e}{\frac{\textcolor{b l a c k}{65}}{2}} = p$

This is the solution. Hope this helped!