Question

Calculati
a l2x-5l=3
b lx-5l=-2
c lx-2l>2

Answer 1

$\displaystyle a).|2x-5|=3 \\ 2x-5=3 \\ 2x=3+5 \\ 2x=8 \\ x= \frac{8}{2} \\ x=4 \\ 2x-5=-3 \\ 2x=-3+5 \\ 2x=2 \\ x= \frac{2}{2} \\ x=1 \\ S=\{1;4\}$
$\displaystyle b).|x-5|=-2 \Rightarrow Nu~are~solutii$
$\displaystyle c).|x-2|\ \textgreater \ 2 \\ x-2\ \textgreater \ 2 \\ x\ \textgreater \ 2+2 \\ x\ \textgreater \ 4 \\ x-2\ \textless \ -2 \\ x\ \textless \ -2+2 \\ x\ \textless \ 0 \\ x \in (- \infty ,0) \cup (4, \infty)$