Question

Solutiile inecuatiilor :
a)| x-1| (|2x-1|-5)<0
b) |2x-1|(7-|2x+1|)>0

Answer 1

a) Produsul a doua numere este negativ daca unul din numere este pozitiv, iar celalat este negativ.
$|x-1}| \geq 0=\ \textgreater \ |2x-1|-5\ \textless \ 0=\ \textgreater \ |2x-1|\ \textless \ 5=\ \textgreater \ \\ =\ \textgreater \ -5\ \textless \ 2x-1\ \textless \ 5=\ \textgreater \ -4\ \textless \ 2x\ \textless \ 6=\ \textgreater \ -2\ \textless \ x\ \textless \ 3=\ \textgreater \ \\ =\ \textgreater \ x\in\{-1;2\}.$
*x=1 nu convine pentru ca atunci ar avea loc egalitate.

b) Produsul a doua numere este pozitiv cand numerele au acelasi semn.
$|2x-1| \geq 0=\ \textgreater \ 7-|2x+1| \ \textgreater \ 0=\ \textgreater \ |2x+1| \ \textless \ 7=\ \textgreater \ \\ =\ \textgreater \ -7\ \textless \ 2x+1\ \textless \ 7=\ \textgreater \ -8\ \textless \ 2x\ \textless \ 6=\ \textgreater \ -4\ \textless \ x\ \textless \ 3=\ \textgreater \ \\ =\ \textgreater \ x\in\{-3;-2;-1;1;2\}.$