Question

for what integers will the sum of 10 times the integer and 4 times the reciprocal be 14?

Answer 1

set up an equation:
10x+4(1/x)=14

then solve for x: (multiply each side by x to get rid of the x in the denominator)
10x^2+4=14x

Then subtract 14x over:
10x^2-14x+4=0

Then FOIL and solve

Answer 2

or the reverse of FOIL

Answer 3

\[10x+4(\frac{1}{x})=14\]
\[10x+\frac{4}{x}=14\]
\[10x^2+4=14x\]
\[10x^2-14x+4=0\]
\[5x^2-7x+2=0\]
\[(5x-2)(x-1)=0\]
\[x=\frac{2}{5} , x=1\]

Answer 4

\( 10x +4/x =14 \implies \left.\left\{x= \frac{2}{5}\right\},\{x= 1\}\right\} \) ony x=1 is the integer hence the answer.