Question

Determinati multimile urmatoare :
A) {X∈N|1≤5X+12/12X+5≤2}
B) {X∈Z|2X+1/5<3X+1/9<4X+1/13}
Vreau rezolvarea completa !

Answer 1

A.
$1\leq \frac{5x+2}{12x+5} \leq 2 \\ \frac{5x+2}{12x+5} \leq 2 \\ 5x+2 \leq 2(12x+5) \\ 5x+2 \leq 24x+10 \\ 2-10 \leq 24x-5x \\ -8 \leq 19x \\ - \frac{8}{19} \leq x \\ x \geq - \frac{8}{19} \\ \frac{5x+2}{12x+5} \geq 1 \\ 5x+2 \geq 12x+5 \\ 2-5 \geq 12x-5x \\ -3 \geq 7x \\ x \leq - \frac{3}{7}$
x∈(-∞;-3/7] reunit cu (-8/19;+∞)