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

The solution to (2|x|)/(1-|x-1|)>= |x+2| is -1+sqrt(5)<= x<2

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

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

- 1 + 5 \leq x < 2

Interval Notation

[- 1 + 5, 2)

Decimal Notation

1.23606 \dots \leq x < 2

Solution steps

\frac{2 ∣ x ∣}{1 - ∣ x - 1 ∣} \geq ∣ 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

No Solution or - 1 + 5 \leq x < 2

Merge Overlapping Intervals

- 1 + 5 \leq x < 2

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