Bepaal de waarde van x.
- \(14x+1=2\)
- \(5x-13=-7\)
- \(8x-6=5\)
- \(11x+4=-10\)
- \(13x-1=13\)
- \(-3x+11=5\)
- \(3x+13=11\)
- \(9x-14=-4\)
- \(x-12=-11\)
- \(13x+14=10\)
- \(-15x+6=-10\)
- \(-2x-3=10\)
Bepaal de waarde van x.
Verbetersleutel
- \(\begin{align} & 14x \color{red}{+1}& = &2 \\\Leftrightarrow & 14x \color{red}{+1}\color{blue}{-1}
& = &2\color{blue}{-1} \\\Leftrightarrow &14x
& = &1\\\Leftrightarrow & \color{red}{14}x
& = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14}
& = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-13}& = &-7 \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13}
& = &-7\color{blue}{+13} \\\Leftrightarrow &5x
& = &6\\\Leftrightarrow & \color{red}{5}x
& = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5}
& = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-6}& = &5 \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6}
& = &5\color{blue}{+6} \\\Leftrightarrow &8x
& = &11\\\Leftrightarrow & \color{red}{8}x
& = &11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8}
& = & \frac{11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{8} } & & \\ & V = \left\{ \frac{11}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+4}& = &-10 \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4}
& = &-10\color{blue}{-4} \\\Leftrightarrow &11x
& = &-14\\\Leftrightarrow & \color{red}{11}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11}
& = & \frac{-14}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-1}& = &13 \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1}
& = &13\color{blue}{+1} \\\Leftrightarrow &13x
& = &14\\\Leftrightarrow & \color{red}{13}x
& = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13}
& = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+11}& = &5 \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11}
& = &5\color{blue}{-11} \\\Leftrightarrow &-3x
& = &-6\\\Leftrightarrow & \color{red}{-3}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3}
& = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+13}& = &11 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13}
& = &11\color{blue}{-13} \\\Leftrightarrow &3x
& = &-2\\\Leftrightarrow & \color{red}{3}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3}
& = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-14}& = &-4 \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14}
& = &-4\color{blue}{+14} \\\Leftrightarrow &9x
& = &10\\\Leftrightarrow & \color{red}{9}x
& = &10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9}
& = & \frac{10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-12}& = &-11 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12}
& = &-11\color{blue}{+12} \\\Leftrightarrow &x
& = &1\\\Leftrightarrow & \color{red}{}x
& = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1}
& = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+14}& = &10 \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14}
& = &10\color{blue}{-14} \\\Leftrightarrow &13x
& = &-4\\\Leftrightarrow & \color{red}{13}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13}
& = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+6}& = &-10 \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6}
& = &-10\color{blue}{-6} \\\Leftrightarrow &-15x
& = &-16\\\Leftrightarrow & \color{red}{-15}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15}
& = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-3}& = &10 \\\Leftrightarrow & -2x \color{red}{-3}\color{blue}{+3}
& = &10\color{blue}{+3} \\\Leftrightarrow &-2x
& = &13\\\Leftrightarrow & \color{red}{-2}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2}
& = & \frac{13}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)