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Popular >

|(x-1)/x |<2

Solution

\frac{x - 1}{x} < 2

Solution

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

+2

Interval Notation

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

Decimal Notation

x < - 1 or x > 0.33333 \dots

Solution steps

\frac{x - 1}{x} < 2

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 2 < \frac{x - 1}{x} < 2

\frac{x - 1}{x} > - 2 and \frac{x - 1}{x} < 2

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

Merge Overlapping Intervals

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

Popular Examples

2 x^{2} + 3 x + 2 = - 3

simplify 3^{2/5}*3^{(-7/5)}simplify

3^{\frac{2}{5}} \cdot 3^{(- \frac{7}{5})}

simplify (9!)/(7!2!)simplify

\frac{9 !}{7 ! 2 !}

1 > \frac{b}{- 2} - 1

simplify (2/(x^3))^3 simplify

(\frac{2}{x ^{3}})^{3}

Frequently Asked Questions (FAQ)

What is |(x-1)/x |<2 ?
The solution to |(x-1)/x |<2 is x<-1\lor x> 1/3