a) (x-1)(x+2) < (x-1)²+3
⇔x²+2x-x-2 < x²-2x+1+3
⇔3x <6
⇔x<2
b) (x+1)²+2x² < (2x+3)²- (x-3)²
⇔x²+2x+1+2x²<4x²+12x+9 - x²+6x-9
⇔ -16x< -1
⇔ x> $\frac{1}{16}$
c) 2x(x-7) +(3-x)²>3.(x+1)²
⇔2x²-14x+9-6x+x²>3(x²+2x+1)
⇔3x²-20x+9>3x²+6x+3
⇔ -26x> -6
⇔ x< $\frac{3}{13}$