Question

||x+2|-5|=3
Apoi a doua
|12-|x-4||=8

Answer 1

Răspuns:

| x+2 |-5=3 ;   | x+2 |-5=-3 ;  }x+2|=8 ;  x+2=8 ; x=6 ;  x+2=-8 ; x=-10 ; |x+2|=2;    x+2=2;x=0 ;  x+2=-2 ; x=-4 ;12-8 =|x-4| ;  x-4=4 ; x=8 ;  x-4=-4 ; x=0

Explicație pas cu pas:

Answer 2

$\Big||x+2|-5\Big| = 3 \\ \\ \Leftrightarrow \left[\begin{array}{lcl} |x+2|-5 = 3 \\\\ |x+2|-5 = -3\end{array}\right. \Leftrightarrow \left[\begin{array}{lcl} \left[\begin{array}{lcl}(x+2)-5 = 3\\-(x+2)-5 = 3 \end{array}\right.\\ \\ \left[\begin{array}{lcl}(x+2)-5 = -3\\-(x+2)-5 = -3 \end{array}\right.\end{array}\right.\Leftrightarrow$

$\Leftrightarrow \left[\begin{array}{lcl} \left[\begin{array}{lcl}x=6\\x=-10\end{array}\right.\\ \\ \left[\begin{array}{lcl}x=0\\x = -4 \end{array}\end{array}\right| \Rightarrow x\in \{-10,-4,0,6\}$

Celălalt se rezolvă la fel.