Z def. wartości bezwzględnej:
|x| = x dla x ≥ 0
|x| = -x dla x < 0
[tex]a) \ |x| = \frac{1}{5}\\\\\underline{x = \frac{1}{5} \ \ \vee \ \ x = -\frac{1}{5}}[/tex]
[tex]b) \ |x| = -2, \ sprzecznosc, \ brak \ rozwiazania\\\\|x| \neq -2[/tex]
[tex]c) \ 3|x| = \sqrt{18}\\\\3|x|= \sqrt{9\cdot2}\\\\3|x| = 3\sqrt{2} \ \ /:3\\\\|x| = \sqrt{2}\\\\\underline{x = \sqrt{2} \ \ \vee \ \ x = -\sqrt{2}}[/tex]
[tex]d) \ 5|x|+10\sqrt{3} = 0\\\\5|x| = -10\sqrt{3} \ \ /:5\\\\|x| = -2\sqrt{3}, \ sprzecznosc, \ brak \ rozwiazania\\\\|x| \neq -2\sqrt{3}[/tex]
[tex]e) \ -\frac{|x|}{3}+1 = 1\\\\-\frac{|x|}{3} = 1-1\\\\-\frac{|x|}{3} = 0 \ \ /\cdot(-3)\\\\|x| = 0\\\\\underline{x = 0}[/tex]
[tex]f) \ \frac{3|x|+1}{2} = 5 \ \ /\cdot2\\\\3|x|+1 = 10\\\\3|x| = 10-1\\\\3|x| = 9 \ \ /:3\\\\|x| = 3\\\\\underline{x = 3 \ \ \vee \ \ x = -3}[/tex]
