Question

Resolva as inequações

2(x+3)-4<3(x-2)




2x+2 - x/4 ≥ x-5/2
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   3

Answer 1

$2(x+3)-4\ \textless \ 3(x-2)\to\\\\ 2x+6-4\ \textless \ -3x-6\to\\\\ 2x+3x\ \textless \ -6-6+4\to\\\\ 5x\ \textless \ -8~\to\\\\ x\ \textgreater \ - \dfrac{8}{5} \\\\\\\\ \boxed{\boxed{S = \{x \epsilon \mathbb{R} \ | \ x\ \textgreater \ - \dfrac{8}{5}}}$





$\dfrac{2x+2}{3} - \dfrac{x}{4} \geq x- \dfrac{5}{2} \to~~ mmc=12\\\\\\ 8x+8-3x \geq 12x-30\to\\\\ 8x-3x-12x \geq -30-8\to \\\\ -7x \geq -38~(-1)\to\\\\ 7x \leq 38\to\\\\ x \leq \dfrac{38}{7} \\\\\\\\ \boxed{\boxed{S = \{x \epsilon \mathbb{R} \ | \ x \leq \dfrac{38}{7} }}$