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Il 2x + 1 I - 5I = 2
Rezolvati in Q acest modul. Cu explicatii, altfel nu se ia in considerare


Răspuns :


[tex]\it ||2x+1|-5|=2 \\\;\\ Notez\ \ 2x+1=y. \\\;\\ Ecua\c{\it t}ia\ devine: \ \ ||y|-5|=2\Leftrightarrow |y| - 5 = \pm2[/tex]

[tex]\it I)\ |y| -5 = -2|_{+5} \Leftrightarrow |y| =3 \Leftrightarrow y=\pm3 \\\;\\ II)\ |y|-5=2|_{+5}\Leftrightarrow\ |y| = 7\Leftrightarrow y=\pm7 \\\;\\ y\in\{-7,\ -3,\ 3,\ 7\}[/tex]

Revin asupra notației :


[tex]\it 2x+1\in\{-7,\ -3,\ 3,\ 7\}|_{-1} \Leftrightarrow2x\in\{-8,\ -4,\ 2,\ 6\}|_{:2}\Leftrightarrow \\\;\\ \Leftrightarrow x\in\{-4,\ -2,\ 1,\ 3\}[/tex]