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Popular >

|(x-3)/(5x)|< 1/3

Solution

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

Solution

x < - \frac{9}{2} or x > \frac{9}{8}

+2

Interval Notation

(- \infty, - \frac{9}{2}) \cup (\frac{9}{8}, \infty)

Decimal Notation

x < - 4.5 or x > 1.125

Solution steps

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

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

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

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

(x < 0 or x > \frac{9}{8}) and (x < - \frac{9}{2} or x > 0)

Merge Overlapping Intervals

x < - \frac{9}{2} or x > \frac{9}{8}

Popular Examples

log_{x-2}(x^2-x)<log_{x-2}(7x+33)

lo g_{x - 2} (x^{2} - x) < lo g_{x - 2} (7 x + 33)

5 (u + 1) > 2 - 3 u

- x^{2} + 2 x - 4 = 0

2 f + 3 = 11 f - 24

x^{2} - 121 \geq 0

Frequently Asked Questions (FAQ)

What is |(x-3)/(5x)|< 1/3 ?
The solution to |(x-3)/(5x)|< 1/3 is x<-9/2 \lor x> 9/8