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Popular >

|(x+1)/x |<4

Solution

\frac{x + 1}{x} < 4

Solution

x < - \frac{1}{5} or x > \frac{1}{3}

+2

Interval Notation

(- \infty, - \frac{1}{5}) \cup (\frac{1}{3}, \infty)

Decimal Notation

x < - 0.2 or x > 0.33333 \dots

Solution steps

\frac{x + 1}{x} < 4

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 4 < \frac{x + 1}{x} < 4

\frac{x + 1}{x} > - 4 and \frac{x + 1}{x} < 4

(x < - \frac{1}{5} or x > 0) and (x < 0 or x > \frac{1}{3})

Merge Overlapping Intervals

x < - \frac{1}{5} or x > \frac{1}{3}

Popular Examples

x^{2} - 2 x - 8 > 2 x

3 ∣ 5 - 2 x ∣ > 7

∣ 7 x - 5 ∣ > - 2

x^{2} - 2 < 1

|2-2x|<x^2-3x+4

∣ 2 - 2 x ∣ < x^{2} - 3 x + 4

Frequently Asked Questions (FAQ)

What is |(x+1)/x |<4 ?
The solution to |(x+1)/x |<4 is x<-1/5 \lor x> 1/3