Question

Determinați mulțimea A = { x aparține Z* | x+3<2x+13 / 3 < x+5 }


AJUTOR !!! DAU COROANA !! ​

Answer 1

Explicație pas cu pas:

$x + 3 < \dfrac{2x + 13}{3} < x + 5 \ \ \ \Big| \cdot 3$

$3(x + 3) < 2x + 13 < 3(x + 5)$

$3x + 9 < 2x + 13 < 3x + 15 \ \ \ \Big| - 13$

$3x - 4 < 2x < 3x + 2 \ \ \ \Big| - 3x$

$- 4 < 2x - 3x < 2$

$- 4 < - x < 2 \ \ \ \Big| \cdot ( - 1)$

$4 > x > - 2 \iff - 2 < x < 4$

$\implies A = \Big\{-1; 1; 2; 3\Big\}$