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

The solution to 3/(|x+3|)>= |x+2| is (-5-sqrt(13))/2 <= x<-3\lor-3<x<= (sqrt(13)-5)/2

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

\frac{3}{∣ x + 3 ∣} \geq ∣ x + 2 ∣

\frac{- 5 - 13}{2} \leq x < - 3 or - 3 < x \leq \frac{13 - 5}{2}

Interval Notation

[\frac{- 5 - 13}{2}, - 3) \cup (- 3, \frac{13 - 5}{2}]

Decimal Notation

- 4.30277 \dots \leq x < - 3 or - 3 < x \leq - 0.69722 \dots

Solution steps

\frac{3}{∣ x + 3 ∣} \geq ∣ x + 2 ∣

Find positive and negative intervals

x < - 3, - 3 \leq x < - 2, x \geq - 2

Solve the inequality for each interval

\frac{- 5 - 13}{2} \leq x < - 3 or - 3 < x < - 2 or - 2 \leq x \leq \frac{13 - 5}{2}

Merge Overlapping Intervals

\frac{- 5 - 13}{2} \leq x < - 3 or - 3 < x \leq \frac{13 - 5}{2}

\frac{5 3}{4 2}

x^{2} + \frac{2}{3} x - \frac{1}{3} = 0

r^{2} + 4 r + 3 = 0

x^{2} + \frac{1}{6} x + 1 = 0

m r + n s - n r - m s

What is 3/(|x+3|)>= |x+2| ?
The solution to 3/(|x+3|)>= |x+2| is (-5-sqrt(13))/2 <= x<-3\lor-3<x<= (sqrt(13)-5)/2