Question

Os numeros inteiros nao positivos que pertencem ao conjunto soluçao da inequaçao x-2/3 menor ou igual 5x+1/9?

Answer 1

$\dfrac{x-2}{3}\le\dfrac{5x+1}{9}$

$\dfrac{x-2}{3}-\dfrac{5x+1}{9}\le0$

$\dfrac{3x-6-5x-1}{9}\le0$

$-2x-7\le0$

$2x+7\ge0$

$x\ge\dfrac{-7}{2}$

$x\ge-3,5$

Como $x\in\mathbb{Z}_{-}$, temos $x\in\{-3,-2,-1\}$.