Bepaal de waarde van x.
- \(14x+9=-14\)
- \(11x+1=1\)
- \(-14x-2=-12\)
- \(13x-3=14\)
- \(-4x+13=5\)
- \(-15x+2=13\)
- \(14x-15=-13\)
- \(-8x+3=12\)
- \(-x+10=-13\)
- \(-12x+1=-14\)
- \(12x+4=15\)
- \(6x-15=5\)
Bepaal de waarde van x.
Verbetersleutel
- \(\begin{align} & 14x \color{red}{+9}& = &-14 \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9}
& = &-14\color{blue}{-9} \\\Leftrightarrow &14x
& = &-23\\\Leftrightarrow & \color{red}{14}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14}
& = & \frac{-23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+1}& = &1 \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1}
& = &1\color{blue}{-1} \\\Leftrightarrow &11x
& = &0\\\Leftrightarrow & \color{red}{11}x
& = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11}
& = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-2}& = &-12 \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2}
& = &-12\color{blue}{+2} \\\Leftrightarrow &-14x
& = &-10\\\Leftrightarrow & \color{red}{-14}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14}
& = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-3}& = &14 \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3}
& = &14\color{blue}{+3} \\\Leftrightarrow &13x
& = &17\\\Leftrightarrow & \color{red}{13}x
& = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13}
& = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+13}& = &5 \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13}
& = &5\color{blue}{-13} \\\Leftrightarrow &-4x
& = &-8\\\Leftrightarrow & \color{red}{-4}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4}
& = & \frac{-8}{-4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+2}& = &13 \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2}
& = &13\color{blue}{-2} \\\Leftrightarrow &-15x
& = &11\\\Leftrightarrow & \color{red}{-15}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15}
& = & \frac{11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-15}& = &-13 \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15}
& = &-13\color{blue}{+15} \\\Leftrightarrow &14x
& = &2\\\Leftrightarrow & \color{red}{14}x
& = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14}
& = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+3}& = &12 \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3}
& = &12\color{blue}{-3} \\\Leftrightarrow &-8x
& = &9\\\Leftrightarrow & \color{red}{-8}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8}
& = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+10}& = &-13 \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10}
& = &-13\color{blue}{-10} \\\Leftrightarrow &-x
& = &-23\\\Leftrightarrow & \color{red}{-}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1}
& = & \frac{-23}{-1} \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+1}& = &-14 \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1}
& = &-14\color{blue}{-1} \\\Leftrightarrow &-12x
& = &-15\\\Leftrightarrow & \color{red}{-12}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12}
& = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+4}& = &15 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4}
& = &15\color{blue}{-4} \\\Leftrightarrow &12x
& = &11\\\Leftrightarrow & \color{red}{12}x
& = &11\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12}
& = & \frac{11}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{12} } & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-15}& = &5 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15}
& = &5\color{blue}{+15} \\\Leftrightarrow &6x
& = &20\\\Leftrightarrow & \color{red}{6}x
& = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6}
& = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)