Vgln. eerste graad (reeks 5)

Alles samen. Gebruik stappenplan en ZRM!

\(5(5x+\frac{3}{11})=8x+\frac{2}{3}\)

\(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{11})& = & 8x+\frac{2}{3} \\\Leftrightarrow & 25x+\frac{15}{11}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+45} & = & \color{red}{264x} +22 \\\Leftrightarrow & 825x \color{red}{+45} \color{blue}{-45} \color{blue}{-264x} & = & \color{red}{264x} +22 \color{blue}{-264x} \color{blue}{-45} \\\Leftrightarrow & 825x-264x& = & 22-45 \\\Leftrightarrow & \color{red}{561} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{561} & & \\ & V = \left\{ \frac{-23}{561} \right\} & \\\end{align}\)