Question

help me ajutatima va rog​

Answer 1

1.

Explicităm modulul:

$\it I)\ \ x-4 < 0 \Rightarrow x < 4\ \ \ \ (1)\\ \\ x-4 < 0 \Rightarrow |x-4|=-x+4,\ iar\ inecua\c{\it t}ia\ devine:\\ \\ -x+4\geq15 \Rightarrow 4-15\geq x \Rightarrow x\leq-11\ \ \ \ (1')\\ \\ (1),\ (1') \Rightarrow x\in(-\infty,\ \ -11]= S_1\\ \\ \\ II)\ x-4\geq0 \Rightarrow x\geq4\ \ \ \ \ (2)\\ \\ x-4\geq0 \Rightarrow |x-4|=x-4,\ iar\ inecua\c{\it t}ia\ devine:\\ \\ x-4\geq15\bigg|_{+4} \Rightarrow x\geq19\ \ \ \ \ (2')\\ \\ (2),\ (2') \Rightarrow x\in[19,\ \infty)=S_2$

Mulțimea soluțiilor inecuației este :

$\it S=S_1\cup S_2=(-\infty,\ -11]\cup [19,\ \ \infty)$