Vgln. eerste graad (reeks 4)

Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

\(\frac{x}{7}-\frac{3}{7}=\frac{-5}{6}x-6\)

\(\text{42 is het kleinste gemene veelvoud van 7, 7 en 6} \\ \begin{align} & \frac{x}{7}-\frac{3}{7}& = & \frac{-5}{6}x-6 \\\Leftrightarrow & \color{blue}{42.} (\frac{6x}{ \color{blue}{42} }- \frac{ 18 }{ \color{blue}{42} })& = & (\frac{-35}{ \color{blue}{42} }x-\frac{252}{ \color{blue}{42} }) \color{blue}{.42} \\\Leftrightarrow & 6x-18& = & -35x-252 \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{+35x} & = & \color{red}{-35x} -252 \color{blue}{+35x} \color{blue}{+18} \\\Leftrightarrow & 41x& = & -234 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = & \frac{-234}{41} \\\Leftrightarrow & x = \frac{-234}{41} & & \\ & V = \left\{ \frac{-234}{41} \right\} & \\\end{align}\)