# Test: Inequalities II - Challenging

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Question 1:   Solve the inequality:  $\frac{4x-4}{x+4}
$x\in \left(-4;+\infty \right)$
$x\in \left(-4;4\right)$
$x\in \left(-6;-5\right)\cup \left(-4;+\infty \right)$
$x\in \left[-4;+\infty \right)$
Question 2:   Solve the inequality:  $\frac{1}{\left|x\right|+1}>1$
$x\in \left(-\infty ;1\right)$
$x=0$
$х\in \varnothing$
$x\in \left(-1;1\right)$
Question 3:   Solve the inequality:  $\left|\frac{1}{x+3}\right|>1$ for $x<-5$
$x\in \left(-4;-3\right)$
$x\in \varnothing$
$x=-4$
$x\in \left[-4;-3\right]$
Question 4:   Solve the inequality:  $\left|{x}^{2}-3x+6\right|\le 6$
$х\in ℝ$
$x\in \left[0;3\right)$
$x\in \left(0;3\right)$
$x\in \left[0;3\right]$
Question 5:   Solve the inequality:  $\sqrt{{x}^{2}-3x-10}
$x\in \left(-\infty ;-\frac{10}{3}\right)$
$x\in \left(-\infty ;-2\right]\cup \left[5;+\infty \right)$
$x\in \left(-\infty ;-\frac{10}{3}\right]$
$x\in \left(-\frac{10}{3};2\right]$
Question 6:   Solve the inequality:  $\frac{{x}^{2}-9x+20}{{x}^{2}-6x+8}<0$
$x\in \left(2;5\right)$
$x\in \left(2;5\right)\\left\{4\right\}$
$x=4$
$x\in \left[2;5\right]\\left\{4\right\}$
Question 7:   Solve the inequality:  $\frac{1}{x+3}>\frac{1}{x-1}$ 
$x\in \left(1;+\infty \right)$
$x\in \left(-\infty ;-3\right)\cup \left(1;+\infty \right)$
$x\in \left(-\infty ;-3\right)$
$x\in \left(-3;1\right)$
Question 8:   Solve the inequality:  $\frac{{x}^{2}-4x-5}{{x}^{2}-11x+30}>0$
$x\in \left(-1;5\right)\cup \left(6;+\infty \right)$
$x\in \left(-\infty ;-1\right)$
$x\in \left(6;+\infty \right)$
$x\in \left(-\infty ;-1\right)\cup \left(6;+\infty \right)$
Question 9:   Solve the inequality:  $\frac{{x}^{2}-4x+4}{x-1}>0$
$x\in \left(-1;-2\right)$
$x\in \left(1;2\right)\cup \left(2;+\infty \right)$
$x\in \left(-1;+\infty \right)$
$x\in \left(2;+\infty \right)$
Question 10:   Solve the inequality:  $\frac{{\left(\sqrt{x}\right)}^{2}+20-{x}^{2}}{x+1}\le 0$
$x\in \left[-4;-1\right]\cup \left[5;+\infty \right)$
$x\in \left[5;+\infty \right)$
$x\in \left(5;+\infty \right)$
$x\in \left[-4;-1\right)\cup \left[5;+\infty \right)$