What is x/2 >= 4/(x+1)+3 ?

The solution to x/2 >= 4/(x+1)+3 is -2 = 7

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x/2 >= 4/(x+1)+3

\frac{x}{2} \geq \frac{4}{x + 1} + 3

- 2 \leq x < - 1 or x \geq 7

Interval Notation

[- 2, - 1) \cup [7, \infty)

Solution steps

\frac{x}{2} \geq \frac{4}{x + 1} + 3

Rewrite in standard form

\frac{x ^{2} - 5 x - 14}{x + 1} \geq 0

Factor

\frac{x ^{2} - 5 x - 14}{x + 1} : \frac{( x + 2 ) ( x - 7 )}{x + 1}

\frac{( x + 2 ) ( x - 7 )}{x + 1} \geq 0

Identify the intervals

- 2 \leq x < - 1 or x \geq 7

y - 23 \geq - 11

(x + 4) (x - 6) < 0

(- 4 b^{2} + 6 b - 9) - (7 b^{2} - 2 b - 5)

x^{2} - 6 x + 8 < 0

\frac{12 !}{( 12 - 7 ) !}

What is x/2 >= 4/(x+1)+3 ?
The solution to x/2 >= 4/(x+1)+3 is -2<= x<-1\lor x>= 7