Vgln. eerste graad (reeks 5)

Alles samen. Gebruik stappenplan en ZRM!

\(3(-4x+\frac{5}{2})=5x+\frac{2}{7}\)

\(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{2})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{15}{2}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{+105} & = & \color{red}{70x} +4 \\\Leftrightarrow & -168x \color{red}{+105} \color{blue}{-105} \color{blue}{-70x} & = & \color{red}{70x} +4 \color{blue}{-70x} \color{blue}{-105} \\\Leftrightarrow & -168x-70x& = & 4-105 \\\Leftrightarrow & \color{red}{-238} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{-238} & & \\\Leftrightarrow & x = \frac{101}{238} & & \\ & V = \left\{ \frac{101}{238} \right\} & \\\end{align}\)