Răspuns:
x ∈ {2; 10}
Explicație pas cu pas:
[tex]|2x - 8| = |x + 2|[/tex]
2x - 8 = 0 => 2x = 8 => x = 8 : 2 => x = 4
x + 2 = 0 => x = -2
dacă: x < -2
|2x - 8| = 8 - 2x
|x + 2| = - x - 2
[tex]8 - 2x = - x - 2 \iff 8 + 2 = - x + 2x \\ x = 10 \not \in \Big(- \infty ; - 2\Big)[/tex]
dacă: -2 ≤ x < 4
|2x - 8| = 8 - 2x
|x + 2| = x + 2
[tex]8 - 2x = x + 2 \iff 8 - 2 = x + 2x \\ 3x = 6 \implies \bf x = 2 \in \Big[ - 2 ; 4\Big)[/tex]
dacă: x ≥ 4
|2x - 8| = 2x - 8
|x + 2| = x + 2
[tex]2x - 8 = x + 2 \iff 2x - x = 2 + 8 \\ \implies \bf x = 10 \in \Big[4 ; + \infty \Big)[/tex]
