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Popular >

|(x+1)/x |< 5/2

Solution

\frac{x + 1}{x} < \frac{5}{2}

Solution

x < - \frac{2}{7} or x > \frac{2}{3}

+2

Interval Notation

(- \infty, - \frac{2}{7}) \cup (\frac{2}{3}, \infty)

Decimal Notation

x < - 0.28571 \dots or x > 0.66666 \dots

Solution steps

\frac{x + 1}{x} < \frac{5}{2}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{5}{2} < \frac{x + 1}{x} < \frac{5}{2}

\frac{x + 1}{x} > - \frac{5}{2} and \frac{x + 1}{x} < \frac{5}{2}

(x < - \frac{2}{7} or x > 0) and (x < 0 or x > \frac{2}{3})

Merge Overlapping Intervals

x < - \frac{2}{7} or x > \frac{2}{3}

Popular Examples

2 - 4 ∣ 2 x + 4 ∣ < - 26

∣ 2 x - a ∣ < 3

x^2+2|x+3|-10<= 0

x^{2} + 2 ∣ x + 3 ∣ - 10 \leq 0

∣ x - 6 ∣ > x^{2} - 5 x + 9

∣ x - 1 ∣ < x^{2} + 1

Frequently Asked Questions (FAQ)

What is |(x+1)/x |< 5/2 ?
The solution to |(x+1)/x |< 5/2 is x<-2/7 \lor x> 2/3