Question

resolva inequação simultânea a seguri: 2 - x ≤ 3x + 2 < 4x + 1

Answer 1

$\mathsf{2-x\le~3x+2\textless~4x+1} \\ \implies\begin{cases}\mathsf{3x+2\ge~2-x}\\\mathsf{3x+2\textless~4x+1}\end{cases}$

$\mathsf{3x+2\ge~2-x}\\\mathsf{3x+x\ge~2-2}\\\mathsf{4x\ge~0}\\\mathsf{x\ge\dfrac{0}{4}}\\\mathsf{x\ge0}$

$\mathsf{s_{1}=\{x\in\mathbb{R}/x\ge0\}}$

$\mathsf{3x+2\textless4x+1}\\\mathsf{3x-4x\textless1-2}\\\mathsf{-x\textless-1\times(-1)}\\\mathsf{x>1}$

$\mathsf{s_{2}=\{x\in\mathbb{R}/x>1\}}$

$\mathsf{s_{1}\cap~s_{2}=\{0\le~x\textless1\}}$

A solução da inequação é

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{s=\{x\in\mathbb{R}/0\le~x\textless1\}}}}}}$