I A Maron Solutions for Chapter: Introduction to Mathematical Analysis, Exercise 1: Real Numbers.The Absolute Value of a Real Number

Determine the values of $x$ satisfying the following equalities: $\left|\frac{x-1}{x+1}\right|=\frac{x-1}{x+1}$;

Determine the values of $x$ satisfying the following equalities:
$\left|x^2-5x+6\right|=-\left(x^2-5x+6\right)$.

Determine the values of $x$ satisfying the following equalities:
.$\left|\left(x^2+4x+9\right)+(2x-3)\right|=\left|x^2+4x+9\right|+|2x-3|$ 

Determine the values of $x$ satisfying the following equalities:
$\left|\left(x^4-4\right)-\left(x^2+2\right)\right|=\left|x^4-4\right|-\left|x^2+2\right|$ 

Solve the inequalities:
$|3 x-5|-|2 x+3|>0$

Solve the inequalities:$\left|x^2-5x\right|>\left|x^2\right|-\left|5x\right|$ 

Find the roots of the following equations :$\left|\sin x\right|=\sin x+1$

Find the roots of the following equations :$x^2-2\left|x\right|-3=0$