abs(ln(x+e))<1 inequation

Given the inequality:
$$\left|{\log{\left(x + e \right)}}\right| < 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{\log{\left(x + e \right)}}\right| = 1$$
Solve:
$$x_{1} = 0$$
$$x_{2} = -2.3504023872876$$
$$x_{1} = 0$$
$$x_{2} = -2.3504023872876$$
This roots
$$x_{2} = -2.3504023872876$$
$$x_{1} = 0$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$-2.3504023872876 + - \frac{1}{10}$$
=
$$-2.4504023872876$$
substitute to the expression
$$\left|{\log{\left(x + e \right)}}\right| < 1$$
$$\left|{\log{\left(-2.4504023872876 + e \right)}}\right| < 1$$

-log(-(2.4504023872876 - E)) < 1

but

-log(-(2.4504023872876 - E)) > 1

Then
$$x < -2.3504023872876$$
no execute
one of the solutions of our inequality is:
$$x > -2.3504023872876 \wedge x < 0$$

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