Question

Se -3 \leq 5 - 2x \leq 7 , então: ????? socorro

Answer 1

$\mathrm{-3\leq5-2x\leq7}\\\\ \mathrm{\Rightarrow Subtraindo\ 5\ de\ todas\ as\ partes\ da\ inequa\c{c}\~ao:}\\\\ \mathrm{-3-5\leq5-2x-5\leq7-5\ \to\ -8\leq-2x\leq2}\\\\ \mathrm{\Rightarrow Multiplicando\ todas\ as\ partes\ por\ (-1)\ \to\ inverte\ a\ desigualdade:}\\\\ \mathrm{-8(-1)\geq-2x(-1)\geq2(-1)\ \to\ 8\geq2x\geq-2}\\\\ \mathrm{\Rightarrow Dividindo\ todas\ as\ partes\ por\ 2:}\\\\ \mathrm{\dfrac{8}{2}\geq\dfrac{2x}{2}\geq\dfrac{-2}{2}\ \to\ \boxed{\mathbf{4\geq x\geq-1}}}$

$\boxed{\boxed{\mathbf{\mathbb{S}=\{x\in\mathbb{R}\ |\ -1\leq x\leq4\}}}}$