Vgln. eerste graad (reeks 5)

Alles samen. Gebruik stappenplan en ZRM!

\(2(-5x-\frac{3}{11})=7x+\frac{8}{11}\)

\(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -10x-\frac{6}{11}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{-6} & = & \color{red}{77x} +8 \\\Leftrightarrow & -110x \color{red}{-6} \color{blue}{+6} \color{blue}{-77x} & = & \color{red}{77x} +8 \color{blue}{-77x} \color{blue}{+6} \\\Leftrightarrow & -110x-77x& = & 8+6 \\\Leftrightarrow & \color{red}{-187} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-187} & & \\\Leftrightarrow & x = \frac{-14}{187} & & \\ & V = \left\{ \frac{-14}{187} \right\} & \\\end{align}\)