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

Răspuns :

[tex] \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} ] [/tex]

[tex] \frac{2-x}{2}\geq \frac{1}{3} [/tex], x∈N

[tex] \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} \\
[/tex]

Stim ca x∈N ⇒ x∈[0, 4/3]