Bepaal de waarde van x.
- \(10x+6=7\)
- \(-13x+13=7\)
- \(3x+12=-7\)
- \(2x-12=-12\)
- \(-5x+3=6\)
- \(x+9=-2\)
- \(9x+7=15\)
- \(-13x+9=-4\)
- \(-14x-6=12\)
- \(-x+13=-2\)
- \(3x+13=-8\)
- \(-11x-9=5\)
Bepaal de waarde van x.
Verbetersleutel
- \(\begin{align} & 10x \color{red}{+6}& = &7 \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6}
& = &7\color{blue}{-6} \\\Leftrightarrow &10x
& = &1\\\Leftrightarrow & \color{red}{10}x
& = &1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10}
& = & \frac{1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+13}& = &7 \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13}
& = &7\color{blue}{-13} \\\Leftrightarrow &-13x
& = &-6\\\Leftrightarrow & \color{red}{-13}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13}
& = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+12}& = &-7 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12}
& = &-7\color{blue}{-12} \\\Leftrightarrow &3x
& = &-19\\\Leftrightarrow & \color{red}{3}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3}
& = & \frac{-19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{3} } & & \\ & V = \left\{ \frac{-19}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-12}& = &-12 \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12}
& = &-12\color{blue}{+12} \\\Leftrightarrow &2x
& = &0\\\Leftrightarrow & \color{red}{2}x
& = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2}
& = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+3}& = &6 \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3}
& = &6\color{blue}{-3} \\\Leftrightarrow &-5x
& = &3\\\Leftrightarrow & \color{red}{-5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5}
& = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+9}& = &-2 \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9}
& = &-2\color{blue}{-9} \\\Leftrightarrow &x
& = &-11\\\Leftrightarrow & \color{red}{}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1}
& = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+7}& = &15 \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7}
& = &15\color{blue}{-7} \\\Leftrightarrow &9x
& = &8\\\Leftrightarrow & \color{red}{9}x
& = &8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9}
& = & \frac{8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+9}& = &-4 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9}
& = &-4\color{blue}{-9} \\\Leftrightarrow &-13x
& = &-13\\\Leftrightarrow & \color{red}{-13}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13}
& = & \frac{-13}{-13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-6}& = &12 \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6}
& = &12\color{blue}{+6} \\\Leftrightarrow &-14x
& = &18\\\Leftrightarrow & \color{red}{-14}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14}
& = & \frac{18}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+13}& = &-2 \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13}
& = &-2\color{blue}{-13} \\\Leftrightarrow &-x
& = &-15\\\Leftrightarrow & \color{red}{-}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1}
& = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+13}& = &-8 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13}
& = &-8\color{blue}{-13} \\\Leftrightarrow &3x
& = &-21\\\Leftrightarrow & \color{red}{3}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3}
& = & \frac{-21}{3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-9}& = &5 \\\Leftrightarrow & -11x \color{red}{-9}\color{blue}{+9}
& = &5\color{blue}{+9} \\\Leftrightarrow &-11x
& = &14\\\Leftrightarrow & \color{red}{-11}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11}
& = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)