Question

acelea incercuite plss

Answer 1

|x|>5=+-6,+-7,+-8,+-9,+-10..

|-x+1|<4=-4,+-3,+-2,+-1,0

|x|>=2 =+-3,+-4,+-5,+-6,+-7,+-8,+-9,+-10...

|x-1|<=4 =5,4,+-3,+-2,+-1,0

|-x+3|>5=-3,-4,-5,-6,-7,-8,+-9,+-10,+-11...

Answer 2

$\it x\in \mathbb{Z}\ \ \ \ \ \ \ (*)\\ \\ h)\ |x-1|\leq4 \Rightarrow -4\leq x-1\leq4|_{+1} \Rightarrow -3\leq x\leq5}\stackrel{(*)}{\Longrightarrow} \\ \\ \Rightarrow x\in\{-3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5\}\\ \\ \\ k)\ |-x+1|<4 \Rightarrow |x-1|<4 \Rightarrow -4< x-1 <4|_{+1} \Rightarrow -3< x <5 \Rightarrow \\ \\ \stackrel{(*)}{\Longrightarrow }\ x\in \{-2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4\}$

$\it j)\ |2x|<8 \Rightarrow 2|x|<8|_{:2} \Rightarrow |x|<4 \Rightarrow -4< x <4\stackrel{(*)}{\Longrightarrow}x\in\{-3,-2,-1,0,\ 1,\ 2,\ 3\}$

$\it d)\ \ |x|\geq2 \Rightarrow S=\mathbb{Z}\setminus A,\ unde\ A=\{x\in\mathbb{Z} \Big{|} \ \ | x | <2 \}\\ \\ |x|<2 \Rightarrow -2< x <2 \stackrel{(*)}{\Longrightarrow}\ x\in\{-1,\ 0,\ 1\}=A\\ \\ S=\mathbb{Z} \setminus \{-1,\ 0,\ 1\}$

$\it \ell)\ |-x+3|>5 \Rightarrow |x-3|>5 \Rightarrow S=\mathbb{Z}\setminus A,\ unde\ A=\{x\in\mathbb{Z}\Big{|}\ |x-3\leq5|\}\\ \\ |x-3|\leq5 \Rightarrow -5\leq x-3 \leq5|_{+3} \Rightarrow -2\leq x \leq8\ \stackrel{(*)}{\Longrightarrow}\\ \\ \Rightarrow A=\{-2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8\}\\ \\ S=\mathbb{Z}\setminus \{-2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8\}$