What is 1/(2*sqrt(5x))<10 ?

The solution to 1/(2*sqrt(5x)) 1/2000

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1/(2*sqrt(5x))<10

\frac{1}{2 \cdot 5 x} < 10

x > \frac{1}{2000}

Interval Notation

(\frac{1}{2000}, \infty)

Decimal Notation

x > 0.0005

Solution steps

\frac{1}{2 5 x} < 10

Multiply both sides by

2

\frac{1 \cdot 2}{2 5 x} < 10 \cdot 2

Simplify

\frac{1}{5 x} < 20

Let

u = 5 x

\frac{1}{u} < 20

\frac{1}{u} < 20 : u < 0 or u > \frac{1}{20}

u < 0 or u > \frac{1}{20}

Substitute back

u = 5 x

5 x < 0 or 5 x > \frac{1}{20}

5 x < 0 :

No Solution for

x \in R

5 x > \frac{1}{20} : x > \frac{1}{2000}

Combine the intervals

No Solution or x > \frac{1}{2000}

Merge Overlapping Intervals

x > \frac{1}{2000}

Find singularity points

Find non-negative values for radicals:

x \geq 0

Combine the intervals

x > \frac{1}{2000} and x \geq 0

Merge Overlapping Intervals

x > \frac{1}{2000}

5 - x^{2} > x - 1

\frac{- ( x + 6 )}{( x - 2 )} < 3

x + 4 x - 4 \geq 0

x^{2} + 3 x + 3 < 2 x + 1

x \geq 4 - x