Vgln. eerste graad (reeks 4)

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

\(\frac{x}{5}+\frac{5}{11}=\frac{7}{6}x-8\)

\(\text{330 is het kleinste gemene veelvoud van 5, 11 en 6} \\ \begin{align} & \frac{x}{5}+\frac{5}{11}& = & \frac{7}{6}x-8 \\\Leftrightarrow & \color{blue}{330.} (\frac{66x}{ \color{blue}{330} }+ \frac{ 150 }{ \color{blue}{330} })& = & (\frac{385}{ \color{blue}{330} }x-\frac{2640}{ \color{blue}{330} }) \color{blue}{.330} \\\Leftrightarrow & 66x+150& = & 385x-2640 \\\Leftrightarrow & 66x \color{red}{+150} \color{blue}{-150} \color{blue}{-385x} & = & \color{red}{385x} -2640 \color{blue}{-385x} \color{blue}{-150} \\\Leftrightarrow & -319x& = & -2790 \\\Leftrightarrow & \frac{-319x}{ \color{red}{-319} }& = & \frac{-2790}{-319} \\\Leftrightarrow & x = \frac{2790}{319} & & \\ & V = \left\{ \frac{2790}{319} \right\} & \\\end{align}\)