What is 5/(sqrt(x))>4 ?

The solution to 5/(sqrt(x))>4 is 0<x< 25/16

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5/(sqrt(x))>4

\frac{5}{x} > 4

0 < x < \frac{25}{16}

Solution steps

\frac{5}{x} > 4

Divide both sides by

5

\frac{\frac{5}{x}}{5} > \frac{4}{5}

Simplify

\frac{1}{x} > \frac{4}{5}

Let

u = x

\frac{1}{u} > \frac{4}{5}

\frac{1}{u} > \frac{4}{5} : 0 < u < \frac{5}{4}

0 < u < \frac{5}{4}

Substitute back

u = x

0 < x < \frac{5}{4}

a < u < b

then

a < u and u < b

0 < x and x < \frac{5}{4}

0 < x : x > 0

x < \frac{5}{4} : x < \frac{25}{16}

Combine the intervals

x > 0 and x < \frac{25}{16}

Merge Overlapping Intervals

0 < x < \frac{25}{16}

Find singularity points

Find non-negative values for radicals:

x \geq 0

Combine the intervals

0 < x < \frac{25}{16} and x \geq 0

Merge Overlapping Intervals

0 < x < \frac{25}{16}

8 + 12 a^{2} + 6 a^{4} + a^{6}

3 s^{2} - 14 s + 8

t^{- \frac{1}{3}}

- 2 m^{2} - 6 = 0

\frac{12 n ^{5}}{36 n}