Bepaal de waarde van x.
- \(6x-13=12\)
- \(15x-4=9\)
- \(2x+4=14\)
- \(14x+5=7\)
- \(-15x-6=13\)
- \(-6x+7=8\)
- \(-12x+1=1\)
- \(6x-13=13\)
- \(8x+12=-2\)
- \(-3x-13=10\)
- \(-7x-11=-11\)
- \(-6x+3=8\)
Bepaal de waarde van x.
Verbetersleutel
- \(\begin{align} & 6x \color{red}{-13}& = &12 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13}
& = &12\color{blue}{+13} \\\Leftrightarrow &6x
& = &25\\\Leftrightarrow & \color{red}{6}x
& = &25\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6}
& = & \frac{25}{6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-4}& = &9 \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4}
& = &9\color{blue}{+4} \\\Leftrightarrow &15x
& = &13\\\Leftrightarrow & \color{red}{15}x
& = &13\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15}
& = & \frac{13}{15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+4}& = &14 \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4}
& = &14\color{blue}{-4} \\\Leftrightarrow &2x
& = &10\\\Leftrightarrow & \color{red}{2}x
& = &10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2}
& = & \frac{10}{2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+5}& = &7 \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5}
& = &7\color{blue}{-5} \\\Leftrightarrow &14x
& = &2\\\Leftrightarrow & \color{red}{14}x
& = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14}
& = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-6}& = &13 \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6}
& = &13\color{blue}{+6} \\\Leftrightarrow &-15x
& = &19\\\Leftrightarrow & \color{red}{-15}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15}
& = & \frac{19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+7}& = &8 \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7}
& = &8\color{blue}{-7} \\\Leftrightarrow &-6x
& = &1\\\Leftrightarrow & \color{red}{-6}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6}
& = & \frac{1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+1}& = &1 \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1}
& = &1\color{blue}{-1} \\\Leftrightarrow &-12x
& = &0\\\Leftrightarrow & \color{red}{-12}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12}
& = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-13}& = &13 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13}
& = &13\color{blue}{+13} \\\Leftrightarrow &6x
& = &26\\\Leftrightarrow & \color{red}{6}x
& = &26\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6}
& = & \frac{26}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+12}& = &-2 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12}
& = &-2\color{blue}{-12} \\\Leftrightarrow &8x
& = &-14\\\Leftrightarrow & \color{red}{8}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8}
& = & \frac{-14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-13}& = &10 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13}
& = &10\color{blue}{+13} \\\Leftrightarrow &-3x
& = &23\\\Leftrightarrow & \color{red}{-3}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3}
& = & \frac{23}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-11}& = &-11 \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11}
& = &-11\color{blue}{+11} \\\Leftrightarrow &-7x
& = &0\\\Leftrightarrow & \color{red}{-7}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7}
& = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+3}& = &8 \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3}
& = &8\color{blue}{-3} \\\Leftrightarrow &-6x
& = &5\\\Leftrightarrow & \color{red}{-6}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6}
& = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)