Question

determinati multimea : A={x€ Z/ 7/2x-7} € Z

Answer 1

2x-7€D7 ;D7={+1;-1;+7;-7} =>2x-7=1=> x=4; 2x-7=-1 =>X=3; 2X-7=7 =>X=7 SI 2X-7=-7 =>X=0 => A={0;3;4;7}

Answer 2

   
[tex]\displaystyle \\A=\{x\in N~|~\frac{7}{2x-7} \in N\}\\\\ \frac{7}{2x-7} \in N ~~\Longrightarrow~~(2x-7) \texttt{ este divizor un al lui 7. }\\\\ \texttt{Divizorii intregi ai lui 7 sunt: } \\ D_7=\{-7;~-1;~1;~7\} \\ \\ \texttt{Rezolvam ecuatiile: } \\ \\ 2x - 7 = -7 ~~\Longrightarrow~~ 2x = -7+7 ~~\Longrightarrow~~2x=0 ~~\Longrightarrow~~x_1=0 \\ \\ 2x - 7 = -1 ~~\Longrightarrow~~ 2x = -1+7 ~~\Longrightarrow~~2x=6 ~~\Longrightarrow~~x_2=3 [/tex]

[tex]2x - 7 = 1 ~~\Longrightarrow~~ 2x = 1+7~~\Longrightarrow~~2x=8 ~~\Longrightarrow~~x_3=4 \\ \\ 2x - 7 = 7~~\Longrightarrow~~ 2x = 7+7~~\Longrightarrow~~2x=14 ~~\Longrightarrow~~x_4=7 \\ \\ \boxed{A = \{0; ~3; ~4; ~7\}}[/tex]