Bepaal de waarde van x.
- \(11x+11=7\)
- \(15x-9=-4\)
- \(-3x-5=-9\)
- \(13x+2=7\)
- \(-6x+4=-13\)
- \(14x+10=-5\)
- \(-5x+14=1\)
- \(3x+2=-6\)
- \(5x+5=-13\)
- \(-x+10=14\)
- \(12x-7=12\)
- \(6x-2=1\)
Bepaal de waarde van x.
Verbetersleutel
- \(\begin{align} & 11x \color{red}{+11}& = &7 \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11}
& = &7\color{blue}{-11} \\\Leftrightarrow &11x
& = &-4\\\Leftrightarrow & \color{red}{11}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11}
& = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-9}& = &-4 \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9}
& = &-4\color{blue}{+9} \\\Leftrightarrow &15x
& = &5\\\Leftrightarrow & \color{red}{15}x
& = &5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15}
& = & \frac{5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-5}& = &-9 \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5}
& = &-9\color{blue}{+5} \\\Leftrightarrow &-3x
& = &-4\\\Leftrightarrow & \color{red}{-3}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3}
& = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+2}& = &7 \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2}
& = &7\color{blue}{-2} \\\Leftrightarrow &13x
& = &5\\\Leftrightarrow & \color{red}{13}x
& = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13}
& = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+4}& = &-13 \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4}
& = &-13\color{blue}{-4} \\\Leftrightarrow &-6x
& = &-17\\\Leftrightarrow & \color{red}{-6}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6}
& = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+10}& = &-5 \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10}
& = &-5\color{blue}{-10} \\\Leftrightarrow &14x
& = &-15\\\Leftrightarrow & \color{red}{14}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14}
& = & \frac{-15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+14}& = &1 \\\Leftrightarrow & -5x \color{red}{+14}\color{blue}{-14}
& = &1\color{blue}{-14} \\\Leftrightarrow &-5x
& = &-13\\\Leftrightarrow & \color{red}{-5}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5}
& = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+2}& = &-6 \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2}
& = &-6\color{blue}{-2} \\\Leftrightarrow &3x
& = &-8\\\Leftrightarrow & \color{red}{3}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3}
& = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+5}& = &-13 \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5}
& = &-13\color{blue}{-5} \\\Leftrightarrow &5x
& = &-18\\\Leftrightarrow & \color{red}{5}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5}
& = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+10}& = &14 \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10}
& = &14\color{blue}{-10} \\\Leftrightarrow &-x
& = &4\\\Leftrightarrow & \color{red}{-}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1}
& = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-7}& = &12 \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7}
& = &12\color{blue}{+7} \\\Leftrightarrow &12x
& = &19\\\Leftrightarrow & \color{red}{12}x
& = &19\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12}
& = & \frac{19}{12} \\\Leftrightarrow & \color{green}{ x = \frac{19}{12} } & & \\ & V = \left\{ \frac{19}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-2}& = &1 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2}
& = &1\color{blue}{+2} \\\Leftrightarrow &6x
& = &3\\\Leftrightarrow & \color{red}{6}x
& = &3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6}
& = & \frac{3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)