Question

Resolva as duas inequações do primeiro grau...

Answer 1

$x- \dfrac{5-x}{6}\ \textgreater \ \dfrac{4x+4}{3}- \dfrac{x}{2} \\ \\ \\ \dfrac{6x-(5-x)}{6}\ \textgreater \ \dfrac{2*(4x+4)}{2*3}- \dfrac{3*x}{3*2} \\ \\ \\ \dfrac{6x-5+x}{6}\ \textgreater \ \dfrac{8x+8}{6}- \dfrac{3x}{6} \\ \\ \\ \dfrac{7x-5}{6}\ \textgreater \ \dfrac{5x+8}{6} \\ \\ \\ 7x-5\ \textgreater \ 5x+8 \\ \\ 7x-5x\ \textgreater \ 8+5\qquad \to 2x\ \textgreater \ 13\qquad \to \boxed{x\ \textgreater \ \frac{13}{2} }\to x\in (\frac{13}{2}; +\infty)$

$\dfrac{x}{2}- \dfrac{x-1}{3} \leq x- \dfrac{x}{6} \\ \\ \\ \dfrac{3x}{6}- \dfrac{2(x-1)}{6} \leq \dfrac{6x-x}{6} \\ \\ \\ \dfrac{3x}{6}- \dfrac{2x-2}{6} \leq \dfrac{6x-x}{6} \\ \\ \\ \dfrac{3x-2x+2}{6} \leq \dfrac{5x}{6} \\ \\ \\ x+2 \leq 5x \\ \\ 2 \leq 4x\qquad \to \frac{2}{4} \leq x\to \boxed{ \frac{1}{2} \leq x\to x\in \left[ \frac{1}{2}, +\infty) }$