Question

o valor de x na equação
$\frac{x}{2} + \frac{x}{3} + \frac{x}{4} = 13$
É:

a) 1
b) 12
c) 13
d) 13/7

ME AJUDEM ​

Answer 1

Vamos começar determinando o MMC dos denominadores no membro esquerdo da equação.

$\begin{array}{c|c}2~,~3~,~4&2\\1~,~3~,~2&2\\1~,~3~,~1&3\\1~,~1~,~1&1\end{array}\\\\\\MMC(2,3,4)~=~2\cdot 2\cdot 3\cdot 1\\\\\boxed{MMC(2,3,4)~=~12}$

Podemos agora proceder com a soma de frações:

$\dfrac{6\cdot x+4\cdot x+3\cdot x}{12}~=~13\\\\\\\dfrac{6x+4x+3x}{12}~=~13\\\\\\6x+4x+3x~=~12\cdot 13\\\\\\13x~=~12\cdot 13\\\\\\x~=~\dfrac{12\cdot 13}{13}\\\\\\\boxed{x~=~12}~~~\Rightarrow~Letra~B\\\\\\\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$