Question

Solutia inecuatiei:
|x-1| (|2x-1| -5) <0 ; x €N*
X=?

Answer 1

x∈N*
x≠1
si
|2x-1|<5


x∈N*
x≠1
si
-5<2x-1<5


x∈N*
x≠1
si
-4<2x<6


x∈N*
x≠1
si
-2<x<3

x∈((-2;3)\{1} )∩N*={2}
x=2

Answer 2

[tex]|x-1|(|2x-1|-5)\ \textless \ 0,x\in \mathbb{N^*}\\ \text{Evident }|x-1|>0\text{pentru }x\neq 1,\text{ceea ce implica faptul ca }\\ |2x-1|-5\ \textless \ 0\\ |2x-1|\ \textless \ 5\\ -5\ \textless \ 2x-1\ \textless \ 5|+1\\ -4\ \textless \ 2x\ \textless \ 6|:2\\ -2\ \textless \ x\ \textless \ 3\\ x\in \mathbb{N^*}\Rightarrow x=2[/tex]