Question

Solutia inecuatiei (2-x)/2 mai mare sau egal decat 1/3, x apartine N

Answer 1

$\frac{2-x}{2} \geq \frac{1}{3} \\ \\ 2-x\geq \frac{2}{3} \\ \\ x-2\leq -\frac{2}{3} |+2\\ \\ x\leq 2-\frac{2}{3} \\ \\ x\leq \frac{4}{3} \\ \\ Ma~rog,~x\geq 0~(natural),~deci~x\in~[0,\frac{4}{3} ]$

Answer 2

$\frac{2-x}{2}\geq \frac{1}{3}$, x∈N

$\frac{2-x}{2}-\frac{1}{3}\geq 0\\ \frac{3(2-x)-2}{6}\geq 0\\ \frac{6-3x-2}{6}\geq 0\\ \frac{4-3x}{6} \geq 0\\ 4-3x\geq 0\\ -3x\geq -4\\ x\leq \frac{4}{3}$

Stim ca x∈N ⇒ x∈[0, 4/3]