Question 141985
Start with the given functions

{{{f(x)=3x-5}}}
{{{g(x)=2x+3}}}



Plug in {{{x=p}}} to evaluate {{{f(p)}}}

{{{f(p)=3p-5}}}



Plug in {{{x=p}}} to evaluate {{{g(p)}}}

{{{g(p)=2p+3}}}


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{{{f(p)=2*g(p)}}} Now move onto the second equation



{{{3p-5=2*g(p)}}} Plug in {{{f(p)=3p-5}}} 



{{{3p-5=2*(2p+3)}}} Plug in {{{g(p)=2p+3}}} 




{{{3p-5=4p+6}}} Distribute



{{{3p=4p+6+5}}}Add 5 to both sides



{{{3p-4p=6+5}}} Subtract 4p from both sides



{{{-p=6+5}}} Combine like terms on the left side



{{{-p=11}}} Combine like terms on the right side



{{{p=(11)/(-1)}}} Divide both sides by -1 to isolate p




{{{p=-11}}} Divide


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Answer:

So our answer is {{{p=-11}}}