Question

Ayuda
6/5(x-1/2) (x-1/3) = x(6x/5+1)​

Answer 1

Respuesta:

$x=\frac{1}{10}$

Explicación paso a paso:

$\frac{6}{5}\left(x-\frac{1}{2}\right)\left(x-\frac{1}{3}\right)=x\left(\frac{6x}{5}+1\right)\\\\\frac{6}{5}\left(x^2-\frac{5}{6}x+\frac{1}{6}\right)=x\left(\frac{6x}{5}+1\right)\\\\\frac{6}{5}x^2-x+\frac{1}{5}=x\left(\frac{6x}{5}+1\right)\\\\\frac{6}{5}x^2-x+\frac{1}{5}=\frac{6x^2}{5}+x\\\\\frac{6}{5}x^2\cdot \:5-x\cdot \:5+\frac{1}{5}\cdot \:5=\frac{6x^2}{5}\cdot \:5+x\cdot \:5$

$6x^2-x\cdot \:5+1=6x^2+x\cdot \:5\\\\6x^2-x\cdot \:5+1-1=6x^2+x\cdot \:5-1\\\\6x^2-x\cdot \:5=6x^2+x\cdot \:5-1\\\\6x^2-x\cdot \:5-\left(6x^2+x\cdot \:5\right)=6x^2+x\cdot \:5-1-\left(6x^2+x\cdot \:5\right)\\\\-10x=-1\\\\\frac{-10x}{-10}=\frac{-1}{-10}\\\\x=\frac{1}{10}$