Question

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

Answer 1

The given expression is

`(4p)/(5)+(1)/(6)=(p)/(10)-(1)/(3)`

First, we subtract p/10 on each side

`\begin{gathered} (4p)/(5)-(p)/(10)+(1)/(6)=(p)/(10)-(p)/(10)-(1)/(3) \\ (4p\cdot10-5\cdot p)/(5\cdot10)+(1)/(6)=-(1)/(3) \\ (40p-5p)/(50)+(1)/(6)=-(1)/(3) \\ (35p)/(50)+(1)/(6)=-(1)/(3) \\ (7p)/(10)+(1)/(6)=-(1)/(3) \end{gathered}`

Then, we subtract 1/6 from each side

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