Question

Aflați cardinal de A
A= {x aparține Z/ | 3x -1 supra 2| < 3 supra 2}

Answer 1

-3/2<(3X-1)/2<3/2; (inmultesti toata relatia cu 2)
-3<3X-1<3; (aduni toata relatia cu +1)
-2<3X<4;(imparti toata relatia la 3)
-2/3<x<4/3 => x apartine (-2/3,4/3), dar x apartine Z => x={0,1}. Sper ca te am ajutat. :)

Answer 2

$A = \Big\{x\in \mathbb_Z \Big\slash \Big| \dfrac{3x-1}{2}\Big| < \dfrac{3}{2} \Big\} \\ \\ \left| \dfrac{3x-1}{2}\right| < \dfrac{3}{2} \\ \\ -\dfrac{3}{2} < \dfrac{3x-1}{2}<\dfrac{3}{2} \Big| \cdot -3 < 3x-1 < 3 \Big|+1 \\ -2 < 3x < 4 \Big| : 3\\ \\ -\dfrac{2}{3} < x < \dfrac{4}{3} \\ \\ x \in \left( -\dfrac{2}{3}; \dfrac{4}{3}\right) \\ \\ x \in \Big( -0,(6); 1,(3) \Big) \\ \\ A = \Big\{0,1\Big\} \\ \\ \boxed{\boxed{ card A = 2 }}$