Question

1/4 (X-2) = 9/5 (X+1/3)

Answer 1

Respuesta:     $x=-\frac{22}{31}\quad \left(\mathrm{Decimal}:\quad x=-0.70967\dots \right)$

Explicación paso a paso:

$\frac{1}{4}\left(x-2\right)=\frac{9}{5}\left(x+\frac{1}{3}\right)$

Desarrollar ambos lados

$\frac{1}{4}x-\frac{1}{2}=\frac{9}{5}x+\frac{3}{5}$

Sumar $\frac{1}{2}$ a ambos lados

$\frac{1}{4}x-\frac{1}{2}+\frac{1}{2}=\frac{9}{5}x+\frac{3}{5}+\frac{1}{2}$

Simplificar

$\frac{1}{4}x=\frac{11}{10}+\frac{9}{5}x$

Restar $\frac{9}{5}x$ de ambos lados

$\frac{1}{4}x-\frac{9}{5}x=\frac{11}{10}+\frac{9}{5}x-\frac{9}{5}x$

Simplificar

$-\frac{31}{20}x=\frac{11}{10}$

Multiplicar ambos lados por 20

$20\left(-\frac{31}{20}x\right)=\frac{11\cdot \:20}{10}$

Simplificar

$-31x=22$

Dividir ambos lados entre -31

$\frac{-31x}{-31}=\frac{22}{-31}$

Simplificar

$x=-\frac{22}{31}$

Espero haberte ayudado :D