|1+x|-1+x=0
|1+x|=[tex] \left \{ {{1+x,1+x \geq 0 } \atop {-(1+x),1+x<0}} \right. [/tex]
|1+x|=[tex] \left \{ {{1+x,x \geq -1} \atop {-1-x, x< -1}} \right. [/tex]
faci tabel
x | -inf -1 +inf
|1+x| | -1-x 0 1+x
Cazul 1: x∈ (-inf; -1)
-1-x-1+x=0
-2=0 (fals)
Solutia= multimea vida
Cazul 2: x∈(-1; +inf)
1+x-1+x=0
2x=0 => x=0 ∈ (-1; +inf)
Solutia: x=0
Analizez capetele:
x=-1⇒ |1-1|-1+1=0
0+0=0(adevarat)
Solutie finala: x∈{-1 ; 0}
