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

The solution to (2|x|)/(1-|x-1|) 2

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(2|x|)/(1-|x-1|)<= |x+2|

\frac{2 ∣ x ∣}{1 - ∣ x - 1 ∣} \leq ∣ x + 2 ∣

x < 0 or 0 < x \leq - 1 + 5 or x > 2

Interval Notation

(- \infty, 0) \cup (0, - 1 + 5] \cup (2, \infty)

Decimal Notation

x < 0 or 0 < x \leq 1.23606 \dots or x > 2

Solution steps

\frac{2 ∣ x ∣}{1 - ∣ x - 1 ∣} \leq ∣ x + 2 ∣

Find positive and negative intervals

x < - 2, - 2 \leq x < 0, 0 \leq x < 1, x \geq 1

Solve the inequality for each interval

x < - 2 or - 2 \leq x < 0 or 0 < x < 1 or 1 \leq x \leq - 1 + 5 or x > 2

Merge Overlapping Intervals

x < 0 or 0 < x \leq - 1 + 5 or x > 2

t - 14 \geq - 28

- \frac{1}{2} + \frac{3}{2}

(y^{- \frac{1}{2}})^{4}

\frac{10 k ^{10}}{( 2 k ^{- 2} ) ^{- 3}}

4 y = 36

What is (2|x|)/(1-|x-1|)<= |x+2| ?
The solution to (2|x|)/(1-|x-1|)<= |x+2| is x<0\lor 0<x<=-1+sqrt(5)\lor x>2