To solve the inequalities, we first need to simplify the expressions on both sides of the inequality signs.

For the first inequality:
X$x+3$ > $x+1$$x-2$ - 1
Expanding the right side:
X^2 + 3X > x^2 - 2x + x - 2 - 1
X^2 + 3X > x^2 - x - 3

Now, let's simplify the second inequality:
$2x+1$$x+2$ - $x-2$$x-4$ Expanding the expression:
2x^2 + 4x + x + 2 - x^2 + 4x - 2x + 8
2x^2 + 5x + 2 - x^2 + 2x + 8
x^2 + 7x + 10

So, the simplified inequalities are:
1) X^2 + 3X > x^2 - x - 3
2) x^2 + 7x + 10