What is (-3)/(|x+1/2 |)<-6 ?

The solution to (-3)/(|x+1/2 |)<-6 is -1<x<-1/2 \lor-1/2 <x<0

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(-3)/(|x+1/2 |)<-6

\frac{- 3}{x + \frac{1}{2}} < - 6

- 1 < x < - \frac{1}{2} or - \frac{1}{2} < x < 0

Solution steps

\frac{- 3}{x + \frac{1}{2}} < - 6

Find positive and negative intervals

x < - \frac{1}{2}, x \geq - \frac{1}{2}

Solve the inequality for each interval

- 1 < x < - \frac{1}{2} or - \frac{1}{2} < x < 0

\frac{∣ x + 3 ∣ + x}{x + 2} > 1

∣ x - 3 ∣ > 2 x + 1

∣ 2 x - 4 ∣ < x - 1

x^{2} - x - 2 > 2

∣ 5 - x ∣ + ∣ x - 13 ∣ < ∣ 2 - x ∣

What is (-3)/(|x+1/2 |)<-6 ?
The solution to (-3)/(|x+1/2 |)<-6 is -1<x<-1/2 \lor-1/2 <x<0