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Popular >

6/(x+3)<x+8

Solution

\frac{6}{x + 3} < x + 8

Solution

- 9 < x < - 3 or x > - 2

+1

Interval Notation

(- 9, - 3) \cup (- 2, \infty)

Solution steps

\frac{6}{x + 3} < x + 8

Rewrite in standard form

\frac{- x ^{2} - 11 x - 18}{x + 3} < 0

Factor

\frac{- x ^{2} - 11 x - 18}{x + 3} : \frac{- ( x + 2 ) ( x + 9 )}{x + 3}

\frac{- ( x + 2 ) ( x + 9 )}{x + 3} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 2 ) ( x + 9 ) ) ( - 1 )}{x + 3} > 0 \cdot (- 1)

Simplify

\frac{( x + 2 ) ( x + 9 )}{x + 3} > 0

Identify the intervals

- 9 < x < - 3 or x > - 2

Popular Examples

18.3-18.3d=-7.8-0.7d+3.22

18.3 - 18.3 d = - 7.8 - 0.7 d + 3.22

-2(x+2)+7=3(x+6)

- 2 (x + 2) + 7 = 3 (x + 6)

x+x/7+1/11 (x+x/7)=60

x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60

4 x^{2} + 7 x = 15

4 x - 2 = 6

Frequently Asked Questions (FAQ)

What is 6/(x+3)<x+8 ?
The solution to 6/(x+3)<x+8 is -9<x<-3\lor x>-2