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

Sagot :

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Solution:

We are given that

[tex] \frac{5}{6} - \frac{1}{3}n = p(5-2n) \\ \frac{5}{6} - \frac{1}{3}n = 5p-2pn[/tex]

By our initial condition, 5p = [tex]\frac{5}{6}[/tex] while -2pn = [tex]-\frac{1}{3}[/tex]. 

[tex]5p = \frac{5}{ \frac{6}{5}} = \frac{5}{30}\\ p = \frac{1}{6} \\ \\ -2pn = -\frac{1}{3}n \\ p= \frac{1}{ \frac{3}{2}} = \frac{1}{6} [/tex]

and we are done as [tex] \frac{5}{6} - \frac{1}{3}n = p(5-2n)[/tex] ⇒ [tex]\frac{5}{6} - \frac{1}{3}n = \frac{5}{6} - \frac{1}{3}n[/tex]
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