What is (|x|)/(|x+2|)<2 ?

The solution to (|x|)/(|x+2|) -4/3

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(|x|)/(|x+2|)<2

\frac{∣ x ∣}{∣ x + 2 ∣} < 2

x < - 4 or x > - \frac{4}{3}

Interval Notation

(- \infty, - 4) \cup (- \frac{4}{3}, \infty)

Decimal Notation

x < - 4 or x > - 1.33333 \dots

Solution steps

\frac{∣ x ∣}{∣ x + 2 ∣} < 2

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 4 or - \frac{4}{3} < x < 0 or x \geq 0

Merge Overlapping Intervals

x < - 4 or x > - \frac{4}{3}

2 6^{2} + b^{2} = 2 15^{2}

- 6 = 23 - 2 x - 5

13 x - 52 = 91

\frac{x}{5} < - 9

(\frac{2 i ^{5} + 3 i ^{17}}{1 + i})^{2}