Question

Rezolvati in Z:
|x|=18
|x-3|=0
|x-5|=1
|x+2|=11
|2x|=8

Answer 1

[tex]\it |a| =b \Longleftrightarrow a = \pm b,\ \ \ \forall b\geq0 [/tex]

[tex]\it |x| = 18 \Leftrightarrow x = \pm18 \Leftrightarrow \begin{cases}\it x_1 = -18 \\ \it x_2 \ =\ 18\end{cases}[/tex]

$\it |x-3| = 0 \Leftrightarrow x-3 = 0 \Leftrightarrow x = 3$

[tex]\it |x-5| = 1 \Leftrightarrow x-5 = \pm1 \Leftrightarrow \begin{cases} \it x-5=-1 \Leftrightarrow x=4 \\ \it x-5\ = \ 1 \Leftrightarrow x = 6 \end{cases}[/tex]