What is |(x+3)/(x+16)|> 3/(x-4) ?

The solution to |(x+3)/(x+16)|> 3/(x-4) is x 10

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|(x+3)/(x+16)|> 3/(x-4)

\frac{x + 3}{x + 16} > \frac{3}{x - 4}

x < - 16 or - 16 < x < 4 or x > 10

Interval Notation

(- \infty, - 16) \cup (- 16, 4) \cup (10, \infty)

Solution steps

\frac{x + 3}{x + 16} > \frac{3}{x - 4}

Find positive and negative intervals

x < - 16, - 16 \leq x < - 3, x \geq - 3

Solve the inequality for each interval

x < - 16 or - 16 < x < - 3 or - 3 \leq x < 4 or x > 10

Merge Overlapping Intervals

x < - 16 or - 16 < x < 4 or x > 10

4 y^{2} - 36

∣ 2 x + 9 ∣ < 5

4 - 6 x > 22

\frac{x + 3}{x - 4} > 0

8 = - \frac{2}{3} h

What is |(x+3)/(x+16)|> 3/(x-4) ?
The solution to |(x+3)/(x+16)|> 3/(x-4) is x<-16\lor-16<x<4\lor x>10