Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(14x-9=1+x\)
- \(2x-1=-9+x\)
- \(12x+12=11+13x\)
- \(-7x-14=-8+x\)
- \(-5x-6=5+x\)
- \(9x+3=4+5x\)
- \(3x+4=-12-2x\)
- \(13x-13=13+x\)
- \(10x+5=-3+7x\)
- \(-2x-7=-5+9x\)
- \(11x+6=-9-2x\)
- \(6x-3=7-11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 14x \color{red}{-9}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-x }
& = & 1 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & 1 \color{blue}{+9} \\\Leftrightarrow &13x
& = &10\\\Leftrightarrow & \color{red}{13}x
& = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-1}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-1}\color{blue}{+1-x }
& = & -9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -9 \color{blue}{+1} \\\Leftrightarrow &x
& = &-8\\\Leftrightarrow & \color{red}{}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -8 \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+12}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-13x }
& = & 11 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & 12x \color{blue}{-13x }
& = & 11 \color{blue}{-12} \\\Leftrightarrow &-x
& = &-1\\\Leftrightarrow & \color{red}{-}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-x }
& = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -8 \color{blue}{+14} \\\Leftrightarrow &-8x
& = &6\\\Leftrightarrow & \color{red}{-8}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-6}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x }
& = & 5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 5 \color{blue}{+6} \\\Leftrightarrow &-6x
& = &11\\\Leftrightarrow & \color{red}{-6}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{6} } & & \\ & V = \left\{ \frac{-11}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+3}& = & 4 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3-5x }
& = & 4 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 9x \color{blue}{-5x }
& = & 4 \color{blue}{-3} \\\Leftrightarrow &4x
& = &1\\\Leftrightarrow & \color{red}{4}x
& = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+4}& = & -12 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4+2x }
& = & -12 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & -12 \color{blue}{-4} \\\Leftrightarrow &5x
& = &-16\\\Leftrightarrow & \color{red}{5}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{-13}\color{blue}{+13-x }
& = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 13x \color{blue}{-x }
& = & 13 \color{blue}{+13} \\\Leftrightarrow &12x
& = &26\\\Leftrightarrow & \color{red}{12}x
& = &26\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{26}{12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+5}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-7x }
& = & -3 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & -3 \color{blue}{-5} \\\Leftrightarrow &3x
& = &-8\\\Leftrightarrow & \color{red}{3}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-7}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-9x }
& = & -5 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -2x \color{blue}{-9x }
& = & -5 \color{blue}{+7} \\\Leftrightarrow &-11x
& = &2\\\Leftrightarrow & \color{red}{-11}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+6}& = & -9 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6+2x }
& = & -9 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 11x \color{blue}{+2x }
& = & -9 \color{blue}{-6} \\\Leftrightarrow &13x
& = &-15\\\Leftrightarrow & \color{red}{13}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-3}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x }
& = & 7 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 7 \color{blue}{+3} \\\Leftrightarrow &17x
& = &10\\\Leftrightarrow & \color{red}{17}x
& = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)