Question

Va rog ajutor rapid dau coroană si 88 de puncte

Answer 1

Răspuns:

Explicație pas cu pas:

Ex1. C, deoarece -2·x>-4 |:(-2), ⇒x<(-4):(-2), ⇒x<2.

Ex2. Produsul este negativ daca factorii au semne diferite, deci

$\left \{ {{5x-2\geq 0} \atop {4x+3\leq0 }} \right. ~~sau~~\left \{ {{5x-2\leq 0} \atop {4x+3\geq 0 }} \right.~~\\1)~\left \{ {{5x-2\geq 0} \atop {4x+3\leq0 }} \right. ~~\left \{ {{5x\geq 2} \atop {4x\leq-3 }} \right. ~~\left \{ {{x\geq \frac{2}{5} } \atop {x\leq -\frac{3}{4} }} \right. ~n-are~solutii\\2)~\left \{ {{5x-2\leq 0} \atop {4x+3\geq 0 }} \right.~~\left \{ {{5x\leq 2} \atop {4x\geq -3 }} \right.~~\left \{ {{x\leq \frac{2}{5} } \atop {x\geq -\frac{3}{4} }} \right.$

Deci x∈[-3/4; 2/5].

Ex3.

$\left \{ {{4x+1\leq 2x+7 } \atop {3x-20<8x-10}} \right. ~~\left \{ {{4x-2x\leq 7-1} \atop {3x-8x<-10+20}} \right. ~~\left \{ {{2x\leq 6} \atop {-5x<10}} \right. ~~\left \{ {{x\leq 3} \atop {x>-2}} \right.$

Deci x∈(-2; 3]

Ex4. Domeniul de definitie se afla din conditiile

$\left \{ {{4x+16\geq 0} \atop {x+3\neq 0}} \right. ~~\left \{ {{4x\geq -16} \atop {x\neq -3}} \right. ~~\left \{ {{x\geq -4} \atop {x\neq -3}} \right.$

Deci Domeniul de definitie este x∈[-4; -3)∪(-3;+∞)