Question

solve for P:4p/5 + 1/6 = p/10 - 1/3

Answer 1

The given expression is

$\frac{4p}{5}+\frac{1}{6}=\frac{p}{10}-\frac{1}{3}$

First, we subtract p/10 on each side

$\begin{gathered} \frac{4p}{5}-\frac{p}{10}+\frac{1}{6}=\frac{p}{10}-\frac{p}{10}-\frac{1}{3} \\ \frac{4p\cdot10-5\cdot p}{5\cdot10}+\frac{1}{6}=-\frac{1}{3} \\ \frac{40p-5p}{50}+\frac{1}{6}=-\frac{1}{3} \\ \frac{35p}{50}+\frac{1}{6}=-\frac{1}{3} \\ \frac{7p}{10}+\frac{1}{6}=-\frac{1}{3} \end{gathered}$

Then, we subtract 1/6 from each side

$\begin{gathered} \frac{7p}{10}+\frac{1}{6}-\frac{1}{6}=-\frac{1}{3}-\frac{1}{6} \\ \frac{7p}{10}=\frac{-6-3}{18} \\ \frac{7p}{10}=\frac{-9}{18} \\ \frac{7p}{10}=-\frac{1}{2} \\ p=-\frac{1\cdot10}{2\cdot7} \\ p=-\frac{5}{7} \end{gathered}$Hence, p = -5/7.