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

The solution to (|x+3|+x)/(x+2)>1 is -5 -1

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(|x+3|+x)/(x+2)>1

\frac{∣ x + 3 ∣ + x}{x + 2} > 1

- 5 < x < - 2 or x > - 1

Interval Notation

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

Solution steps

\frac{∣ x + 3 ∣ + x}{x + 2} > 1

Find positive and negative intervals

x < - 3, x \geq - 3

Solve the inequality for each interval

- 5 < x < - 3 or - 3 \leq x < - 2 or x > - 1

Merge Overlapping Intervals

- 5 < x < - 2 or x > - 1

∣ x - 3 ∣ > 2 x + 1

∣ 2 x - 4 ∣ < x - 1

x^{2} - x - 2 > 2

∣ 5 - x ∣ + ∣ x - 13 ∣ < ∣ 2 - x ∣

∣ x ∣ + ∣ x - 4 ∣ > 4

What is (|x+3|+x)/(x+2)>1 ?
The solution to (|x+3|+x)/(x+2)>1 is -5<x<-2\lor x>-1