What is 1/x >= |x+2| ?

The solution to 1/x >= |x+2| is 0<x<=-1+sqrt(2)

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1/x >= |x+2|

\frac{1}{x} \geq ∣ x + 2 ∣

0 < x \leq - 1 + 2

Interval Notation

(0, - 1 + 2]

Decimal Notation

0 < x \leq 0.41421 \dots

Solution steps

\frac{1}{x} \geq ∣ x + 2 ∣

Find positive and negative intervals

x < - 2, x \geq - 2

Solve the inequality for each interval

No Solution or 0 < x \leq - 1 + 2

Merge Overlapping Intervals

0 < x \leq - 1 + 2

\frac{( x ^{2} - 1 )}{( x ^{2} + x + 1 )} > 1

∣ x + 3 ∣ < 0.01

∣ x - 1 ∣ > 2 ∣ x - 4 ∣

\frac{( 3 x - 5 )}{2} \geq 7

∣ 1 - x ∣ - ∣ 4 + x ∣ < 0