a) [latex]|x| geq 1 \ x geq 1 lub x leq - 1 \ Zatem:\ x in (-infty; - 1 angle cup langle 1; +infty)[/latex] b) [latex]|x| leq 2 \ |x| leq 2 i x geq - 2 \ Zatem:\ x in langle -2; 2 angle[/latex] c) [latex]x| leq 0 \ |x| leq 0 i x geq 0 \ x = 0 \\ Zatem:\ x in {0}[/latex] d) [latex]|x-2| > 1 \ x - 2 > 1 lub x - 2 < - 1 \\ x - 2 > 1 \ x> 1 + 2 \ x > 3 \\ x - 2 < - 1 \ x < - 1 + 2 \ x < 1 \\ Zatem:\ x in (-infty; 1) cup (3; +infty)[/latex] e) [latex]|x-1| < 3 \ x - 1 < 3 i x - 1> - 3 \\ x - 1 < 3 \ x < 3 + 1 \ x < 4 \\ x - 1> - 3 \ x < - 3 + 1 \ x < -2 \\ Zatem:\ x in (-2; 4)[/latex] f) [latex]|x| = 8 \ x = 8 lub x = - 8 \\ Zatem: \ x in {-8; 8 }[/latex] g) [latex]|x+2| = 3 \ x + 2 = 3 lub x + 2 = - 3 \\ x + 2 = 3 \ x = 3 - 2 \ x = 1 \\ x + 2 = - 3 \ x = - 3 - 2 \ x = -5 \\ Zatem: \ x in {-5; 1}[/latex]
