Vgln. eerste graad (reeks 5)

Alles samen. Gebruik stappenplan en ZRM!

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

\(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{3})& = & -3x+\frac{4}{9} \\\Leftrightarrow & -8x+\frac{16}{3}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{48}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+48} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -72x \color{red}{+48} \color{blue}{-48} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{-48} \\\Leftrightarrow & -72x+27x& = & 4-48 \\\Leftrightarrow & \color{red}{-45} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-45} & & \\\Leftrightarrow & x = \frac{44}{45} & & \\ & V = \left\{ \frac{44}{45} \right\} & \\\end{align}\)