Question

Sendo x um numero racional, rezolva equaçao a seguir: 1/3x+1/2=0,2x+0,1333...

Answer 1

Primeiro temos que transformar a dízima 0,133... em uma fração:

$x=0,133..\\10x=1,333...\\100x=13,333\\\\100x-10x=13,333-1,333\\90x=12\\x= \frac{12^{\div6}}{90^{\div6}}=\ \textgreater \ \boxed{x=\frac{2}{15} }$

Agora seguimos os cálculos:

$\frac{x}{3}+ \frac{1}{2}=0,2x+0,1333...\\\\ \frac{x}{3}+ \frac{1}{2}= \frac{2x}{10}+ \frac{2}{15}\\\\ \frac{2x+(3\cdot1)}{6}= \frac{(15\cdot2x)+(10\cdot2)}{150}\\\\ \frac{2x+3}{6}= \frac{30x+20}{150}\\\\ 150\cdot(2x+3)=6\cdot(30x+20)\\\\300x+450=180x+120\\\\ 300x-180x=120-450\\\\ 120x=-330\\\\x=- \frac{330^{\div30}}{120^{\div30}} \\\\\boxed{\boxed{x= -\frac{11}{4}\ ou\ -2,75 }}$