Question

Solve algebraically for the positive value of x, x ≠ 0, and check: 2x+5/7=1/x

Answer 1

\[\frac{2x+5}{7}=\frac{1}{x}\]
\[x(2x+5)=7\]
\[2x^2+5x-7=0\]
\[x=\frac{-5 \pm \sqrt{25-4(2)(-7)}}{2(2)}\]
\[x=\frac{-5 \pm \sqrt{81}}{4}=\frac{-5 \pm 9}{4}=1, \frac{-7}{2}\]
You only want the positive x, so discard x=-7/2

Answer 2

oh i see. thank you

Answer 3

(2x+5)/7 = 1/x
(2x+5) x = 7
2x² + 5x - 7 = 0
( x -1) ( 2x + 7) = 0
=> x = 1 ( Omit x = -7/2)