Question

Resolva o sistema {2x - 1 > 5 e - x - 3 < 0}, em IR.

Answer 1

$\large\boxed{\begin{array}{l}\rm Resolva\,o\,sistema\begin{cases}\sf2x-1>5\\\sf-x-3<0\end{cases}~~~~~~,em~\mathbb{R}:\\\tt a)~\sf x\geqslant3~~~~\tt b)~\sf x>-3~~~~\tt c)~\sf x\leqslant3\end{array}}$

$\Large\boxed{\begin{array}{l}\begin{cases}\sf 2x-1\geqslant5~\boldsymbol I\\\sf -x-3<0~\boldsymbol {II}\end{cases}\\\boldsymbol I:\\\sf 2x-1\geqslant5\\\sf 2x\geqslant5+1\\\sf 2x\geqslant6\\\sf x\geqslant\dfrac{6}{2}\\\\\sf x\geqslant3\\\sf S_1=\{x\in\mathbb{R}/ x\geqslant3\}\\\boldsymbol{II}\\\sf -x-3<0\\\sf -x<3\cdot(-1)\\\sf x>-3\\\sf S_2=\{x\in\mathbb{R}/x>-3\}\\\sf S_1\cap S_2=\{x\in \mathbb{R}/ x\geqslant3\}\\\sf S=S_1\cap S_2\\\sf S=\{x\in\mathbb{R}/x\geqslant3\}\end{array}}$