Question

ajudem nessa inequação!

x + 2 _ x-1 < x
____ ___
3 2

Answer 1

$\frac{x+2}{3} - \frac{x-1}{2} \ \textless \ x \\ \\ mmc(3,2)=6 \\ \\ 2(x+2)-3(x-1)\ \textless \ 6x \\ \\ 2x+4-3x+3\ \textless \ 6x \\ \\ 2x-3x-6x\ \textless \ -4-3 \\ \\ 2x-9x\ \textless \ -7 \\ \\ -7x\ \textless \ -7 \\ \\ 7x\ \textgreater \ 7 \\ \\ x\ \textgreater \ 7\div7 \\ \\ x\ \textgreater \ 1$

na inequação quando a variável for negativa troca-se os sinais

logo o < passa ser >

Answer 2

$\dfrac{x+2}{3} - \dfrac{x-1}{2} \ \textless \ x \\ \\ \\ \dfrac{2(x+2)}{6} - \dfrac{3(x-1)}{6} \ \textless \ x \\ \\ \\2x+4-3x+3\ \textless \ 6x \\ \\ -x+7\ \textless \ 6x \\ \\ 7\ \textless \ 6x+x \\ \\ \\ 7\ \textless \ 7x\qquad \dfrac{7}{7}\ \textless \ x \qquad \boxed{1\ \textless \ x\to x\in (1; +\infty) }$