Question

qual o conjunto solução do sistema de inequacao {3x - 1 > 5x+ 2}
{ 4x+3 < 7x-11​

Answer 1

S= Vazio

Explicação passo-a-passo:

$S=\left\{ \begin{aligned} 3x - 1 > 5x+ 2 \\ 4x+3 < 7x-11\end{aligned} \right. \\ \\ S=\left\{ \begin{aligned} 3x - 1 - 5x - 2 > 0\\ 4x+3 - 7x + 11 < 0\end{aligned} \right. \\ \\ S=\left\{ \begin{aligned} - 2x -3 > 0\\- 3x + 14 < 0\end{aligned} \right. \\ \\ S=\left\{ \begin{aligned} - 2x -3 > 0 \: \: \times ( - 3)\\- 3x + 14 < 0 \: \: \times (2)\end{aligned} \right. \\ \\ S=\left\{ \begin{aligned} 6x + 9 < 0\\- 6x + 28< 0\end{aligned} \right. \\ \\ S=\left\{ \begin{aligned} 6x < - 9\\- 6x < - 28\end{aligned} \right. \\ \\ S=\left\{ \begin{aligned} x < \frac{ - 9}{6} \\x > \frac{ - 28}{ - 6} \end{aligned} \right. \\ \\ S=\left\{ \begin{aligned} x < - \frac{ 3}{2} \\x > \frac{ 14}{ 3} \end{aligned} \right. \\ \\ S=\left\{ \begin{aligned} x < -1,5\\x > 4,6... \: \end{aligned} \right. \\ \\ \boxed{\boxed{\underbrace{{S=\emptyset }}}}$