help me systems of equations and inequalities

[CATIAP]

16-4x^2>0
-3x^2<0
x^2-2x-3<0


(x+1)^2>3(x+2)+1
(x-1)^2+x(1-x)>2+(1-x)(x+1)
(1-x)^2<=1

[Math Tutor]

Can you solve at least one?

[Shpresim]

16-4x^2>0
-3x^2<0
x^2-2x-3<0


(x+1)^2>3(x+2)+1
(x-1)^2+x(1-x)>2+(1-x)(x+1)
(1-x)^2<=1

16-4x^2>0
-4x^2>-16 (divide by -4, the inequality sign changes)
x^2<4
-2<x<2

-3x^2<0 (divide by -3, the inequality sign changes)
x^2>0
we see that for any x the equation stays true
so the interval with solutions is (-∞,∞)

x^2-2x-3<0 (factor the left side of the inequality)
(x-3)(x+1)<0
-1<x<3