What is x/2 >= (25)/(x+1)+2 ?

The solution to x/2 >= (25)/(x+1)+2 is -6 = 9

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x/2 >= (25)/(x+1)+2

\frac{x}{2} \geq \frac{25}{x + 1} + 2

- 6 \leq x < - 1 or x \geq 9

Interval Notation

[- 6, - 1) \cup [9, \infty)

Solution steps

\frac{x}{2} \geq \frac{25}{x + 1} + 2

Rewrite in standard form

\frac{x ^{2} - 3 x - 54}{x + 1} \geq 0

Factor

\frac{x ^{2} - 3 x - 54}{x + 1} : \frac{( x + 6 ) ( x - 9 )}{x + 1}

\frac{( x + 6 ) ( x - 9 )}{x + 1} \geq 0

Identify the intervals

- 6 \leq x < - 1 or x \geq 9

t^{2} - 6 t + 8 = 0

\frac{2 x}{3} - \frac{5 x - 7}{6} = \frac{x}{2} + \frac{5}{3}

3 ∣ p + 2 ∣ \geq 6

3 x^{2} - 6 x y - 5 x + 10 y

y^{2} - x^{2} + 8 y + 16

What is x/2 >= (25)/(x+1)+2 ?
The solution to x/2 >= (25)/(x+1)+2 is -6<= x<-1\lor x>= 9