Question

E URGENT!!
|x-1| (|2x-1|-5)<0

Answer 1

| x-1 | (|2x-1|-5)<0
|x-1| ≥0
⇒ |2x-1|-5 <0
⇒|2x-1|<5
⇔ -5<2x-1<5  /+1
⇔ -4<2x<6  /*1/2
⇔-2<x<3
daca x ∈ Z ,x ∈{-1,0,1,2}
 daca x ∈R,x ∈ (-2,3)

Answer 2

$|x-1| (|2x-1|-5)\ \textless \ 0\\ \\ \boxed{1}\quad |x-1| \geq0 ,\quad \forall x\in \mathbb_{R} \\ \\ Singura conditie care ne intereseaza la |x-1| este sa fie diferit de 0. \\ \\ |x-1| \neq 0 \Rightarrow x-1\neq 0 \Rightarrow x \neq 1 \\ \\ \boxed{2}\quad Cum |x-1| \ \textgreater \ 0, trebuie sa punem conditia pentru |2x-1|-5, \\ sa fie \ \textless \ 0. \\ \\ \\ |2x-1|-5\ \textless \ 0 \Big|+5 \Rightarrow |2x-1| \ \textless \ 5 \Rightarrow -5\ \textless \ 2x-1\ \textless \ 5 \Big|+1 \Rightarrow \\ \\ \Rightarrow -4\ \textless \ 2x\ \textless \ 6\Big|:2 \Rightarrow -2\ \textless \ x\ \textless \ 3 \Rightarrow x\in (-2,3)$


$\\ Din \boxed{1} \cap \boxed{2} \Rightarrow \boxed{x\in (-2,1)\cup(1,3)}\rightarrow \it solutie~ finala.$