Answer
$\left\{x\ |\ x \lt -11 \right\}$ or $\left(-\infty,-11\right)$
Work Step by Step
$(x-1)(x+1) \gt (x-3)(x+4)$
$x^{2}-1 \gt x^{2}+x-12 \qquad$ ... add $1-x-x^{2}$
$-x \gt -11\qquad$ ... multiply with $-1 $ (negative)
... the inequality changes direction ...
$x \lt -11$
Solution set: $\left\{x\ | x \lt -11 \right\}$ or $\left(-\infty,-11\right)$
