Question

O valor de x na equação 3(X−1)+ 2.3(x+ 1)−3(x) =16/27 é:

Obs.: os que estão em parenteses, na verdade estão no expoente.

Se possível, expliquem como chegaram no resultado. Obg

Answer 1

$3^{x-1}~+~2\,.\,3^{x+1}~-~3^x~=~\frac{16}{27}\\\\\\(3^x\,.\,3^{-1})~+~2\,.\,(3^x~\,.\,3^1)~-~3^x~=~\frac{16}{27}\\\\\\Colocando~o~fator~3^x~em~evidencia:\\\\\\3^x~.~\left(3^{-1}~+~2\,.\,3^1~-~1\right)~=~\frac{16}{27}\\\\\\3^x~.~\left(\frac{1}{3}~+~6~-~1\right)~=~\frac{16}{27}\\\\\\3^x~.~\left(\frac{16}{3}\right)~=~\frac{16}{27}\\\\\\3^x~=~\frac{16}{27}~.~\frac{3}{16}\\\\\\3^x~=~\frac{3}{27}\\\\\\3^x~=~\frac{1}{9}\\\\\\3^x~=~3^{-2}\\\\\\\boxed{x~=~-2}$