Question

Como resolvo essa equação (imagem)?

Answer 1

$\dfrac{x}{6}+\dfrac{x}{12}+\dfrac{x}{7}+5+\dfrac{x}{2}+4=x\\ \\ \dfrac{x}{6}+\dfrac{x}{12}+\dfrac{x}{7}+\dfrac{x}{2}+9-x=0\\ \\ \dfrac{x}{6}+\dfrac{x}{12}+\dfrac{x}{7}+\dfrac{x}{2}-x=-9$


Tirando o mmc de todos os denominadores, encontramos

$m.m.c.\left(6,\,12,\,7,\,2 \right )=84$


Multiplicando os dois lados da equação por $84$, temos

$\dfrac{84x}{6}+\dfrac{84x}{12}+\dfrac{84x}{7}+\dfrac{84x}{2}-84x=-9 \cdot 84\\ \\ 14x+7x+12x+42x-84x=-9 \cdot 84\\ \\ \left(14+7+12+42-84 \right )x=-9 \cdot 84\\ \\ -9x=-9 \cdot 84\\ \\ x=\dfrac{-9 \cdot 84}{-9}\\ \\ \boxed{x=84}$

Answer 2

$\dfrac{x}{6} + \dfrac{x}{12} + \dfrac{x}{7} + 5 + \dfrac{x}{2} + 4 = x$

MMC  = 84

$\dfrac{14x + 7x + 12x +84*5 + 42x + 84*4}{84} = 84x \\ \\ \\ 14x + 7x + 12x +84*5 + 42x + 84*4 = 84x \\ \\ \\ 14x + 7x + 12x +420 + 42x + 336 = 84x \\ \\ \\ 75x + 756 = 84x \\ \\ \\ 75x - 84x = -756 \\ \\ \\ -9x = -756 (-1) \\ \\ \\ 9x = 756 \\ \\ \\ x = \dfrac{756}{9} \\ \\ \\ => x = 84$