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

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

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

\frac{( ∣ x + 2 ∣ + x )}{( x + 1 )} > 1

- 3 < x < - 1 or x > - 1

Interval Notation

(- 3, - 1) \cup (- 1, \infty)

Solution steps

\frac{∣ x + 2 ∣ + x}{x + 1} > 1

Find positive and negative intervals

x < - 2, x \geq - 2

Solve the inequality for each interval

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

Merge Overlapping Intervals

- 3 < x < - 1 or x > - 1

∣ x + 7 ∣ + ∣ x ∣ \leq \frac{1}{2}

x^{2} - 5 x + 6 < x^{2} - 2 x

x^{2} - 1 > 0

\frac{( ∣ x ∣ - 3 )}{( ∣ x ∣ - 5 )} < 0

∣ 3 x - 4 ∣ < ∣ 2 x - 1 ∣

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