Question

determine a solução desta equação: $\frac{1-2y}{3}$= $\frac{5-y}{4}$ - 3

Answer 1

$\underbrace{Veja:}$

$\implies~~\sf \dfrac{1-2y}{3}=\dfrac{5-y}{4}-3$

$\implies~~\sf \dfrac{1-2y}{3}=\dfrac{5-y}{4}-\dfrac{3}{1}$

> MMC (3 , 4 , 1) = 12

• Coloque 12 no lugar dos denominadores
• Divida 12 pelo antigo denominador e multiplique pelo numerador

$\implies~~\sf \dfrac{12\div3\cdot(1-2y)}{12}=\dfrac{12\div4\cdot(5-y)}{12}-\dfrac{12\div1\cdot3}{12}$

$\implies~~\sf \dfrac{4\cdot(1-2y)}{12}=\dfrac{3\cdot(5-y)}{12}-\dfrac{12\cdot3}{12}$

$\implies~~\sf \dfrac{4-8y}{12}=\dfrac{15-3y}{12}-\dfrac{36}{12}$

• Denominadores iguais podemos anular

$\implies~~\sf \dfrac{4-8y}{\backslash\!\!\!\!\!12}=\dfrac{15-3y}{\backslash\!\!\!\!\!12}-\dfrac{36}{\backslash\!\!\!\!\!12}$

$\implies~~\sf 4-8y=15-3y-36$

$\implies~~\sf -8y+3y=15-36-4$

$\implies~~\sf -5y=-25~~~\cdot(-1)$

$\implies~~\sf 5y=25$

$\implies~~\sf y=\dfrac{25}{5}$

 $\therefore~~~~\sf y=5$

$~~$

Conjunto solução:

$\boxed{\sf S=\left\{~~5~~\right\}}$