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

The solution to ((|x+4|+2x))/(x+1)>2 is -6 -1

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((|x+4|+2x))/(x+1)>2

\frac{( ∣ x + 4 ∣ + 2 x )}{x + 1} > 2

- 6 < x < - 2 or x > - 1

Interval Notation

(- 6, - 2) \cup (- 1, \infty)

Solution steps

\frac{∣ x + 4 ∣ + 2 x}{x + 1} > 2

Find positive and negative intervals

x < - 4, x \geq - 4

Solve the inequality for each interval

- 6 < x < - 4 or - 4 \leq x < - 2 or x > - 1

Merge Overlapping Intervals

- 6 < x < - 2 or x > - 1

∣ x - 3 ∣ - ∣ x + 2 ∣ \leq 3

\frac{3 - ( 5 x - 2 )}{4} \leq 8

\frac{∣ x - 3 ∣}{∣ x + 1 ∣} \leq 1

x^{3} - 1 \geq 1 - x

∣ x ∣ < 2

What is ((|x+4|+2x))/(x+1)>2 ?
The solution to ((|x+4|+2x))/(x+1)>2 is -6<x<-2\lor x>-1