What is x/2 >= (35)/(x+1)+1 ?

The solution to x/2 >= (35)/(x+1)+1 is -8 = 9

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x/2 >= (35)/(x+1)+1

\frac{x}{2} \geq \frac{35}{x + 1} + 1

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

Interval Notation

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

Solution steps

\frac{x}{2} \geq \frac{35}{x + 1} + 1

Rewrite in standard form

\frac{x ^{2} - x - 72}{x + 1} \geq 0

Factor

\frac{x ^{2} - x - 72}{x + 1} : \frac{( x + 8 ) ( x - 9 )}{x + 1}

\frac{( x + 8 ) ( x - 9 )}{x + 1} \geq 0

Identify the intervals

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

g^{2} - 2 g - 63

\frac{x ^{2} ( 5 + x ) ( x + 6 )}{( x + 7 ) ( x - 3 )} \geq 0

\frac{3 x}{2} + x = \frac{1}{3}

(x - 4)^{2} = 25

x^{2} + 22 = - 12 x

What is x/2 >= (35)/(x+1)+1 ?
The solution to x/2 >= (35)/(x+1)+1 is -8<= x<-1\lor x>= 9