# Test: Inequalities I - Ambitious

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Question 1:   Solve the inequality:  $3{x}^{2}-3x\left(x+7\right)\ge 21$
$x\in \left(-1;1\right]$
$x\in \left(-\infty ;-1\right)$
$x\in \left(-3;-1\right]$
$x\in \left(-\infty ;-1\right]$
Question 2:   Solve the inequality:  $\frac{x+2}{3x-1}\le 1$
$x\in \left(-\infty ;\frac{1}{3}\right]\cup \left(\frac{3}{2};+\infty \right)$
$x\in \left(-\infty ;-\frac{1}{3}\right]\cup \left[\frac{2}{3};+\infty \right)$
$x\in \left(-\infty ;\frac{1}{3}\right)\cup \left[\frac{3}{2};+\infty \right)$
$x\in \left(-\infty ;\frac{1}{3}\right]\cup \left[\frac{3}{2};+\infty \right)$
Question 3:   Solve the inequality:  $\left|2x-3\right|\le 2$
$x\in \left(1;\frac{5}{2}\right)$
$x\in \left(\frac{1}{2};\frac{5}{2}\right)$
$x\in \left[\frac{1}{2};\frac{5}{2}\right]$
$x\in \left(\frac{1}{2};1\right)$
Question 4:   Solve the inequality:  ${x}^{2}-x-16\ge 4$
$x\in \left(-\infty ;4\right]\cup \left(5;+\infty \right)$
$x\in \left(-\infty ;-4\right)\cup \left(5;+\infty \right)$
$x\in \left(-\infty ;-4\right]\cup \left[5;+\infty \right)$
$x\in \left(-4;5\right)$
Question 5:   Solve the inequality:  $\frac{{x}^{2}-5x+6}{x-2}<0$
$x\in \left(-\infty ;3\right)\\left\{2\right\}$
$x\in \left(-\infty ;3\right)$
$x\in \left(-1;3\right)\\left\{2\right\}$
$x\in \left(-\infty ;3\right]\\left\{2\right\}$
Question 6:   Solve the inequality:  $\frac{{x}^{2}}{x-3}<1$
$x\in \left(-\infty ;3\right)$
$x\in \left[-3;3\right]$
$x\in \left(-3;3\right)$
$x\in \left(-\infty ;3\right]$
Question 7:   Solve the inequality:  $\sqrt{2x-3}<9$
$x\in \left(\frac{3}{2};42\right)$
$x\in \left(-\infty ;42\right)$
$x\in \left[1;42\right)$
$x\in \left[\frac{3}{2};42\right)$
Question 8:   Solve the inequality:  ${x}^{2}+7x>0$
$x\in \left(-\infty ;-7\right)$
$x\in \left(0;+\infty \right)$
$x\in \left(-\infty ;-7\right]\cup \left[0;+\infty \right)$
$x\in \left(-\infty ;-7\right)\cup \left(0;+\infty \right)$
Question 9:   Solve the inequality:  $\frac{5-x}{4x-16}\le 0$
$x\in \left(-\infty ;4\right)\cup \left[5;+\infty \right)$
$x\in \left(-\infty ;4\right]\cup \left[5;+\infty \right)$
$x\in \left(-\infty ;4\right)$
$x\in \left[5;+\infty \right)$
Question 10:   Solve the inequality:  $\frac{\left(x+2\right)\left(x-1\right)}{{x}^{2}+1}<0$
$x\in \left(-2;1\right)$
$x\in \left(-2;1\right]$
$x\in \left[-2;1\right)$
$x\in \left[-2;1\right]$