Vgln. eerste graad (reeks 5)

Alles samen. Gebruik stappenplan en ZRM!

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

\(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{2})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{15}{2}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{+45} & = & \color{red}{30x} +4 \\\Leftrightarrow & 72x \color{red}{+45} \color{blue}{-45} \color{blue}{-30x} & = & \color{red}{30x} +4 \color{blue}{-30x} \color{blue}{-45} \\\Leftrightarrow & 72x-30x& = & 4-45 \\\Leftrightarrow & \color{red}{42} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{42} & & \\ & V = \left\{ \frac{-41}{42} \right\} & \\\end{align}\)