How to solve an inequality such as $P=Pr\left[\frac{|X-1|}{X+1}\leq \frac{Q^{-1}(\eta)}{\sqrt{N}}\right]$?

Question

I have an equation given by $$P=Pr\left[\frac{|X-1|}{X+1}\leq \frac{Q^{-1}(\eta)}{\sqrt{N}}\right]$$ How to proceed to solve such inequality? Its answer is given as $$Pr[\lambda_1 \leq X \leq \lambda_2]$$ where $$\lambda_1 = \frac{2}{1+\frac{Q^{-1}(\eta)}{\sqrt{N}}}-1 \qquad \lambda_2 = \frac{2}{1-\frac{Q^{-1}(\eta)}{\sqrt{N}}}-1$$ Any help in this regard is highly appreciated.