Irrational Inequalities: Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
$\sqrt{2x - 5} < 3$
Problem 2
$\sqrt{x + 6} < x - 6$
Problem 3
$\sqrt{3x-7} > 3$
Problem 4
$\sqrt{x^2+5x+4} < x+2$
Problem 5
$\sqrt{x^2-3x-10} < 8-x$
Problem 6
$\sqrt{x^2+x-12} < 6-x$
Problem 7
$\sqrt{7-3x} < -9$
Problem 8
$\sqrt{x+2} > 2x-2$
Problem 9
$\sqrt{x+2} > x$
Problem 10
$x-3 < \sqrt{x+27}$

Problem 11
$\sqrt{4x-8} > -5$
Problem 12
$\sqrt{-x^2+6x-5} > 8-2x$
Problem 13
$\sqrt{2x+1} + \sqrt{x+1} < 1$
Problem 14
$\sqrt{5x-4} + \sqrt{3x+1} < 3$
Problem 15
$\sqrt{1+x} + \sqrt{1-x} > 1$
Problem 16
$\sqrt{x^2+3x+2} - \sqrt{x^2-x+1} < 1$
Problem 17
$\sqrt{2(x+24)} - \sqrt{x-7} \ge \sqrt{x+7}$
Problem 18
$(x+2)\sqrt{x^2-2x-3} \ge 0$
Problem 19
$\frac{\sqrt{5-4x}+7x-6}{x} \ge 2 $
Problem 20
$\sqrt{\frac{x^2-4x+3}{x^2-3x+2}} \le 1$
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