Vgln. eerste graad (reeks 4)

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

\(\frac{x}{4}+\frac{2}{9}=\frac{5}{3}x+8\)

\(\text{36 is het kleinste gemene veelvoud van 4, 9 en 3} \\ \begin{align} & \frac{x}{4}+\frac{2}{9}& = & \frac{5}{3}x+8 \\\Leftrightarrow & \color{blue}{36.} (\frac{9x}{ \color{blue}{36} }+ \frac{ 8 }{ \color{blue}{36} })& = & (\frac{60}{ \color{blue}{36} }x+\frac{288}{ \color{blue}{36} }) \color{blue}{.36} \\\Leftrightarrow & 9x+8& = & 60x+288 \\\Leftrightarrow & 9x \color{red}{+8} \color{blue}{-8} \color{blue}{-60x} & = & \color{red}{60x} +288 \color{blue}{-60x} \color{blue}{-8} \\\Leftrightarrow & -51x& = & 280 \\\Leftrightarrow & \frac{-51x}{ \color{red}{-51} }& = & \frac{280}{-51} \\\Leftrightarrow & x = \frac{-280}{51} & & \\ & V = \left\{ \frac{-280}{51} \right\} & \\\end{align}\)