Question

Ex 12 , va rog dau coroană ​

Answer 1

Explicație pas cu pas:

$\dfrac{3x - 2}{ - 5} < - 2 \ \ \ \Big| \cdot ( - 5)$

$3x - 2 > 10 \iff 3x > 10 + 2$

$3x > 12 \ \ \ \Big| : 3 \implies x > 4 \\ \iff \bf x \in \Big(4 ; +\infty \Big)$

b)

$\dfrac{5(x + 1) + 3(1 - 2x)}{ - 6} \geqslant - \dfrac{1}{2} \ \ \ \Big| \cdot ( - 6)$

$5(x + 1) + 3(1 - 2x) \leqslant 3$

$5x + 5 + 3 - 6x \leqslant 3$

$8 - x \leqslant 3 \iff 8 - 3 \leqslant x$

$\implies x \geqslant 5 \iff \bf x \in \Big[5 +\infty \Big)$

c)

$\dfrac{4x + 8}{ - 3} \geqslant 0$

$- 3 \leqslant 0 \implies 4x + 8 \leqslant 0$

$4x \leqslant - 8 \ \ \ \Big| : 4$

$\implies x \leqslant - 2 \iff \bf x \in \Big(-\infty ; -2 \Big]$

d)

$\dfrac{ - 3}{4x + 8} \geqslant 0 \iff \dfrac{4x + 8}{ - 3}\leqslant 0$

$- 3 \leqslant 0 \implies 4x + 8 \geqslant 0$

$4x \geqslant - 8 \ \ \ \Big| : 4$

$\implies x \geqslant - 2 \iff \bf x \in \Big[-2 ; +\infty \Big)$