Question

No universo Z, quantas são as soluções da inequação | x - 2 | menor ou igual a 3 ?
a) Sete
b) Oito
c) Dez
d) Infinitas
e) Menos que sete

Answer 1

$|x-2|\geq3\\\\\\\begin{matrix}+(x-2)\geq3\\\\x-2\geq3\\\\x\geq3+2\\\\x\geq5\\\\\\\boxed{S'=\{x\in\mathbb{Z}\ |\ x\geq5\}}\end{matrix}\qquad\qquad\qquad\qquad\begin{matrix}-(x-2)\geq3\\\\-x+2\geq3\\\\x\leq2-3\\\\x\leq-1\\\\\\\boxed{S''=\{x\in\mathbb{Z}\ |\ x\leq-1\}}\end{matrix}\\\\\\\\S=S'\cup{S''}\\\\\boxed{\boxed{S=\{x\in\mathbb{Z}\ |\ x\leq-1\ ou\ x\geq5\}}}\\\\\text{Alternativa d).}$