Question

O conjunto solução S, em R, para o sistema de inequações −4 < −x + 2 ≤ 8 é:​

Answer 1

$\boxed{\begin{array}{l}\sf -4<-x+2\leqslant8\longrightarrow\begin{cases}\sf -x+2>-4~~(I)\\\sf -x+2\leqslant8~~(II)\end{cases}\\\underline{\rm Soluc_{\!\!,}\tilde ao~da~desigualdade~I:}\\\sf -x+2>-4\\\sf -x>-4-2\\\sf -x>-6\cdot(-1)\\\sf x<6\\\sf S_{I}=\{x\in\mathbb{R}/x<6\}\\\underline{\rm Soluc_{\!\!,}\tilde ao~da~desigualdade~II:}\\\sf -x+2\leqslant8\\\sf -x\leqslant8-2\\\sf -x\leqslant6\cdot(-1)\\\sf x\geqslant-6\\\sf S_{II}=\{x\in\mathbb{R}/x\geqslant-6\}\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm Fazendo~a~intersecc_{\!\!,}\tilde ao}\\\underline{\rm entre~as~soluc_{\!\!,}\tilde oes~temos:}\\\sf S=\{x\in\mathbb{R}/-6\leqslant x<6\}\end{array}}$