Vgln. eerste graad (reeks 4)

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

\(\frac{x}{5}-\frac{4}{7}=\frac{-8}{3}x+6\)

\(\text{105 is het kleinste gemene veelvoud van 5, 7 en 3} \\ \begin{align} & \frac{x}{5}-\frac{4}{7}& = & \frac{-8}{3}x+6 \\\Leftrightarrow & \color{blue}{105.} (\frac{21x}{ \color{blue}{105} }- \frac{ 60 }{ \color{blue}{105} })& = & (\frac{-280}{ \color{blue}{105} }x+\frac{630}{ \color{blue}{105} }) \color{blue}{.105} \\\Leftrightarrow & 21x-60& = & -280x+630 \\\Leftrightarrow & 21x \color{red}{-60} \color{blue}{+60} \color{blue}{+280x} & = & \color{red}{-280x} +630 \color{blue}{+280x} \color{blue}{+60} \\\Leftrightarrow & 301x& = & 690 \\\Leftrightarrow & \frac{301x}{ \color{red}{301} }& = & \frac{690}{301} \\\Leftrightarrow & x = \frac{690}{301} & & \\ & V = \left\{ \frac{690}{301} \right\} & \\\end{align}\)