What is (20(x-2)}{(x^2+1)}<\frac{-1)/2 ?

The solution to (20(x-2)}{(x^2+1)}<\frac{-1)/2 is -20-sqrt(479)<x<-20+sqrt(479)

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(20(x-2)}{(x^2+1)}<\frac{-1)/2

\frac{20 ( x - 2 )}{( x ^{2} + 1 )} < \frac{- 1}{2}

- 20 - 479 < x < - 20 + 479

Interval Notation

(- 20 - 479, - 20 + 479)

Decimal Notation

- 41.88606 \dots < x < 1.88606 \dots

Solution steps

\frac{20 ( x - 2 )}{x ^{2} + 1} < \frac{- 1}{2}

Rewrite in standard form

\frac{x ^{2} + 40 x - 79}{x ^{2} + 1} < 0

Factor

x^{2} + 40 x - 79 : (x + 20 - 479) (x + 20 + 479)

\frac{( x + 20 - 479 ) ( x + 20 + 479 )}{x ^{2} + 1} < 0

Identify the intervals

- 20 - 479 < x < - 20 + 479

x^{2} (x - 2) (x - 3) (1 - x) (1 + x) \geq 0

\frac{1}{( x ^{2} - 5 x + 6 )} \geq \frac{1}{2}

(x - 1) (x^{2} - 2 x + 1) > 0

3 x^{2} - 27 > 0

x^{3} - 6 x \leq 0

What is (20(x-2)}{(x^2+1)}<\frac{-1)/2 ?
The solution to (20(x-2)}{(x^2+1)}<\frac{-1)/2 is -20-sqrt(479)<x<-20+sqrt(479)