arctg(x)>=1 inequation

Given the inequality:
$$\operatorname{atan}{\left(x \right)} \geq 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\operatorname{atan}{\left(x \right)} = 1$$
Solve:
$$x_{1} = \tan{\left(1 \right)}$$
$$x_{1} = \tan{\left(1 \right)}$$
This roots
$$x_{1} = \tan{\left(1 \right)}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \tan{\left(1 \right)}$$
=
$$- \frac{1}{10} + \tan{\left(1 \right)}$$
substitute to the expression
$$\operatorname{atan}{\left(x \right)} \geq 1$$
$$\operatorname{atan}{\left(- \frac{1}{10} + \tan{\left(1 \right)} \right)} \geq 1$$

-atan(1/10 - tan(1)) >= 1

but

-atan(1/10 - tan(1)) < 1

Then
$$x \leq \tan{\left(1 \right)}$$
no execute
the solution of our inequality is:
$$x \geq \tan{\left(1 \right)}$$

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