Question

qual o conjunto solução da equação x+2/4 - x-2/6 = 2/3 + x?

a) 11/2
b) - 2/11
c) 2/11
d) - 11/2

Answer 1

$x + \dfrac{2}{4} - x - \dfrac{2}{6} = \dfrac{2}{3} + x \\ \\ \\ \dfrac{4x + 2}{4} - \dfrac{6x - 3}{6} = \dfrac{2 + 3x}{3} \\ \\ \\ \dfrac{3x + 1}{2} - \dfrac{3x + 1}{3} = \dfrac{2 + 3x}{3} \\ \\ \\ \dfrac{6x + 3 - 6x - 2}{6} = \dfrac{2 + 3x}{3} \\ \\ \\ \dfrac{1}{6} = \dfrac{2 + 3x}{3} \\ \\ \\ 3 = 6(3x + 2) \\ \\ 3 = 18x + 12 \\ \\ -18x = 12 - 3 (-1) \\ \\ 18x = -12 + 3 \\ \\ 18x = -9 \\ \\ x = \dfrac{-9}{18} \\ \\ \\=\ \textgreater \ x = - \dfrac{1}{2}$