What is sqrt((4x-1)/x)<2 ?

The solution to sqrt((4x-1)/x) = 1/4

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sqrt((4x-1)/x)<2

\frac{4 x - 1}{x} < 2

x \geq \frac{1}{4}

Interval Notation

[\frac{1}{4}, \infty)

Decimal Notation

x \geq 0.25

Solution steps

\frac{4 x - 1}{x} < 2

Square both sides

(\frac{4 x - 1}{x})^{2} < 2^{2}

Simplify

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

4 - \frac{1}{x} < 4 : x > 0

x > 0

Find singularity points

Find non-negative values for radicals:

x < 0 or x \geq \frac{1}{4}

Combine the intervals

x > 0 and (x < 0 or x \geq \frac{1}{4})

Merge Overlapping Intervals

x \geq \frac{1}{4}

80 \cdot \frac{1}{4}

16 x^{2} - y^{2}

1^{\frac{4}{3}}

\frac{k}{3} < - 1

100 + 50 w \geq 18000