Question

Rezolvati in R inecuatia

$|x-1|+|x+1|\leq 4$

Answer 1

$|x-1|+|x+1|\leq 4\\ \\\\\boxed{1} \quad x\in[1,+\infty): \\\\ (x-1)+(x+1)\leq 4 \Rightarrow 2x \leq 4 \Rightarrow x\leq 2 \Rightarrow x\in [1,2] \\ \\\boxed{2}\quad x\in(-1,1):\\ \\ -(x-1)+(x+1)\leq 4 \Rightarrow 2 \leq 4\,\,(A)\Rightarrow x\in (-1,1) \\ \\ \boxed{3}\quad x\in(-\infty,-1]:\\ \\-(x-1)-(x+1)\leq 4 \Rightarrow -2x \leq 4 \Rightarrow -x \leq 2 \Rightarrow\\\\ \Rightarrow x\geq -2 \Rightarrow x \in [-2,-1]$

$\\ \\\text{Din }\,\boxed{1}\,\text{ sau }\,\boxed{2}\,\text{ sau }\,\boxed{3}\,\Rightarrow S = [1,2]\cup(-1,1)\cup[-2,-1]\Rightarrow \\ \\\\ \Rightarrow \boxed{S =\big[-2,2\,\big]}$

Answer 2

Răspuns:

Explicație pas cu pas: