Question

Zadanie 2 w załączniku proszę zróbcie to w miarę prostym sposobem

Answer 1

Odpowiedź:

[tex]zad.2~~\\\\\\\huge\boxed{~~Odp:~~C,~~~~x\in < -4;-2 > ~~}[/tex]

Szczegółowe wyjaśnienie:

   

      [tex]\huge\boxed{~~\mid x\mid =\left \{ {{x~~dla~~x\geq 0} \atop {-x~~dla~~x < 0}} \right. ~~}[/tex]

[tex]\mid ax+b\mid < c[/tex] zapisujemy:[tex]ax+b < c~~\land~~ax+b > -c~~\Rightarrow~~-c < ax+b < c[/tex]

[tex]\mid ax+b\mid > c[/tex] zapisujemy: [tex]ax+b > c~~\lor~~ax+b < -c[/tex]

Rozwiązanie:

zad. 2

[tex]\mid x+3 \mid~ \leq ~1\\\\x+3~\leq ~1~~\land~~x+3~\geq ~-1\\\\~~~~~~~~~~~~~~~\Downarrow\\\\-1\leq x+3\leq 1~~\mid -3\\\\-1-3~\leq~ x+3-3~\leq ~1-3\\\\\huge\boxed{~~-4~\leq ~x~\leq~ -2~~\Rightarrow~~x\in < -4;-2 > ~~}[/tex]