Question

O conjunto-solução da inequação x-(x-3)/2>2x/3 sendo U = R:
a) x<9 b) x=9 c) x>9 d) x≤9 e) x≥9

Answer 1

$x-\dfrac{(x-3)}{2}\ \textgreater \ \dfrac{2x}{3}\\\\\\x-\dfrac{(x-3)}{2}-\dfrac{2x}{3}\ \textgreater \ 0\\\\\\\dfrac{6\cdot{x}}{6}-\dfrac{3\cdot(x-3)}{6}-\dfrac{2\cdot2x}{6}\ \textgreater \ 0\\\\\\\dfrac{6x}{6}-\dfrac{3x-9}{6}-\dfrac{4x}{6}\ \textgreater \ 0\\\\\\\dfrac{6x-(3x-9)-4x}{6}\ \textgreater \ 0\\\\\\\dfrac{6x-3x+9-4x}{6}\ \textgreater \ 0\\\\\\\dfrac{9-x}{6}\ \textgreater \ 0\\\\9-x>6\cdot0\\\\9-x>0\\\\x<9\\\\\\\boxed{S=\{x\in\mathbb{R}\ |\ x<9\}}$