Question

Rezolvati in N inecuatia $(\sqrt{2}-1,5)x \geq 2 \sqrt{2} -3$ 50 de puncte+coroana celui mai desfasurat raspuns

Answer 1

[tex]( \sqrt{2} -1,5)x \geq 2 \sqrt{2} -3 \\ x \geq \frac{2 \sqrt{2} -3 }{ \sqrt{2} -1,5} \\ x \geq \frac{(2 \sqrt{2} -3)(\sqrt{2} +1,5) }{ (\sqrt{2} -1,5)(\sqrt{2} +1,5)} \\ x \geq \frac{4+3 \sqrt{2}-3 \sqrt{2} -4.5 }{2-2.25} \\ x \geq \frac{-0.5}{-0.25} \\ x \geq \frac{5}{10} * \frac{100}{25} \\ x \geq \frac{1}{2} *4 \\ x \geq 2 \\ x\in[2,+ \infty)[/tex]

Answer 2

$( \sqrt{2} -1,5) \geq 2( \sqrt{2} -1,5) \\ \sqrt{2} \ \textless \ 1,42\ \textless \ 1,5 \\ \sqrt{2} -1,5\ \textless \ 0 \\ ( \sqrt{-1,5) } \geq 2( \sqrt{2}-1,5)|:( \sqrt{2} -1,5) \\ x \leq 2 \\ x\in\{0,1,2\}$
Se schimba sensul inegalitatii deoarece am impartit la un numar negativ