Resolver $\dfrac{x}{5}+\dfrac{3}{10}=\dfrac{1-x}{15}-\dfrac{x+3}{30}$

Enunciado:
Resolver:
$$\dfrac{x}{5}+\dfrac{3}{10}=\dfrac{1-x}{15}-\dfrac{x+3}{30}$$

Resolución:
  $\dfrac{x}{5}+\dfrac{3}{10}=\dfrac{1-x}{15}-\dfrac{x+3}{30}$

    $30\cdot \dfrac{x}{5}+30\cdot \dfrac{3}{10}=30\cdot \dfrac{1-x}{15}-30\cdot \dfrac{x+3}{30}$     ( multiplicando por el mmc(5,10,15,30)=30 )

      $\dfrac{30}{5}\,x+\dfrac{30}{10}\cdot 3=\dfrac{30}{15}\,(1-x)-\dfrac{30}{30}\,(x+3)$

        $6\,x+3\cdot 3=2\,(1-x)-1 \cdot (x+3)$

          $6\,x+9=2-2\,x-x-3$

            $6\,x+2\,x+x=2-3-9$

              $9\,x=-10$

                $x=-\dfrac{10}{9}$

$\square$

[nota del autor]