A fast solution of $\frac{\left|x^2-1\right|-3}{1-2x}<\:x$

It can’t be D as

$$\lim\limits_{x \to -\infty} \frac{|x^2-1|-3}{1-2x}= \infty$$

Therefore for large negative values of $x$, $\frac{|x^2-1|-3}{1-2x}$ will be positive and the requested inequality can’t be satisfied. This allows to drop down option D that contains the interval $(-\infty,-1)$.

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Algebra Precalculus

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