Alles samen. Gebruik stappenplan en ZRM!
\(-5(5x-\frac{5}{13})=x+\frac{9}{13}\)
\(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\
\begin{align}
& \color{red}{-5} (5x-\frac{5}{13})& = & x+\frac{9}{13} \\\Leftrightarrow & -25x+\frac{25}{13}& = & x+\frac{9}{13} \\ & & & \text{kgv van noemers 13 en 13 is 13} \\\Leftrightarrow & \color{blue}{13} .(-25x+\frac{25}{13})& = & (x+\frac{9}{13}). \color{blue}{13} \\\Leftrightarrow & -325x \color{red}{+25} & = & \color{red}{13x} +9 \\\Leftrightarrow & -325x \color{red}{+25} \color{blue}{-25} \color{blue}{-13x} & = & \color{red}{13x} +9 \color{blue}{-13x} \color{blue}{-25} \\\Leftrightarrow & -325x-13x& = & 9-25 \\\Leftrightarrow & \color{red}{-338} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-338} & & \\\Leftrightarrow & x = \frac{8}{169} & & \\ & V = \left\{ \frac{8}{169} \right\} & \\\end{align}\)
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vanhoeckes.be/wiskunde 2024-10-22 00:43:43