Question

Enter the value of p so the expression 5/6-1/3nis equivalent to p(5-2n).

Answer 1

Solution:

We are given that


`(5)/(6) - (1)/(3)n = p(5-2n) \\ (5)/(6) - (1)/(3)n = 5p-2pn`

By our initial condition, 5p =
`(5)/(6)` while -2pn =
`-(1)/(3)`.


`5p = (5)/( (6)/(5)) = (5)/(30)\\ p = (1)/(6) \\ \\ -2pn = -(1)/(3)n \\ p= (1)/( (3)/(2)) = (1)/(6)`

and we are done as
`(5)/(6) - (1)/(3)n = p(5-2n)` ⇒
`(5)/(6) - (1)/(3)n = (5)/(6) - (1)/(3)n`