Question 1135796
let a number be {{{x}}}
then it’s reciprocal  is {{{1/x}}}


Twice a number:{{{2x}}}

 +3 times  it’s reciprocal: {{{2x+3(1/x)}}}

  is seven:{{{2x+3(1/x)=7}}}


{{{2x+3(1/x)=7}}}............solve for {{{x}}}


{{{2x+3/x=7}}}........both sides multiply by {{{x}}}

{{{2x^2+3=7x}}}

{{{2x^2-7x+3=0}}}

{{{2x^2-x-6x+3=0}}}

{{{(2x^2-x)-(6x-3)=0}}}

{{{x(2x-1)-3(2x-1)=0}}}

{{{(x - 3) (2 x - 1) = 0}}}

solutions:

{{{x=3}}}

{{{x=1/2}}}