Rozwiąż równania i nierówności z wartością bezwzględną: a) |1-2x|=13 b) ||x-3|+1|=9 c) 2x+|x-3|=0 d) |5x-3|>2 e) |x|-1[latex] leq [/latex]2 f) ||x-1|-3|| [latex] geq [/latex] 4 g) [latex] sqrt{ x^{2} -6x+9} leq 9-|2x-6|[/latex]

[latex]|1-2x|=13\ 1-2x=13 vee 1-2x=-13\ -2x=12 vee -2x=-14\ oxed{x=-6 vee x=7}\\ ||x-3|+1|=9\ |x-3|+1=9 vee |x-3|+1=-9\ |x-3|=8 vee |x-3|=-10\ x-3 =8 vee x-3=-8\ oxed{x=11 vee x=-5}\\ 2x+|x-3|=0\ xin(-infty-3 angle\ 2x-x+3=0\ x=-3\ xin(3,infty)\ 2x+x-3=0\ 3x=3\ x=1\ 1 ot in(3,infty)\ oxed{x=-3} [/latex] [latex]|5x-3|>2\ 5x-3>2 vee5x-3<-2\ 5x>5 vee 5x<1\ x>1 vee x-3\ oxed{xinlangle-3,3 angle}\\ ||x-1|-3|geq4\ |x-1|-3geq4 vee |x-1|-3leq-4\ |x-1|geq7 vee |x-1|leq-1\ x-1geq7 vee x-1leq-7\ xgeq8 vee xleq-6\ oxed{xin(-infty,-6 angle cup langle8,infty)} [/latex] [latex]sqrt{x^2-6x+9}leq9-|2x-6|\ sqrt{(x-3)^2}leq9-2|x-3|\ |x-3|leq9-2|x-3|\ 3|x-3|leq9\ |x-3|leq3\ x-3 leq 3 wedge x-3geq-3\ xleq6 wedge xgeq0\ oxed{xinlangle0,6 angle }[/latex]