Question

resolva o sistema de inequações.

Answer 1

$\left\{\begin{array}{ll}\dfrac{x}{3} - \dfrac{x -2}{5} \ \textless \ 2 (I) \\\dfrac{3(x+6)}{4} \ \textgreater \ 0 (II)\end{array}\right \\ \\ Da\ equa\c{c}\~ao (I) temos:\\ \dfrac{5x - 3x + 6}{15} \ \textless \ 2 \Rightarrow \dfrac{2x + 6 - 30}{15} \ \textless \ 0 \Rightarrow 2x -24 \ \textless \ 0 \Rightarrow x\ \textless \ 12$
$Da \ equa\c{c}\~ao \ (II) \ temos:\\ x - 6 \ \textgreater \ 0 \Rightarrow x \ \textgreater \ 6 \\ Logo, os \ valores \ de \ x \ que \ satisfazem \ o \ sistema\ est\~ao \ no \ intervalo$
$\boxed{6\ \textless \ x\ \textless \ 12}}$