Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(x-9=10+15x\)
- \(-13x+3=-11+x\)
- \(6x+14=12+11x\)
- \(-4x+12=15+13x\)
- \(14x-4=10+x\)
- \(-2x-8=-9+x\)
- \(-8x+5=-9+x\)
- \(-12x+6=-8+x\)
- \(-13x-12=12+x\)
- \(-x+11=7+7x\)
- \(13x+7=11-6x\)
- \(2x+3=3+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & x \color{red}{-9}& = & 10 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-15x }
& = & 10 \color{red}{ +15x }\color{blue}{+9-15x } \\\Leftrightarrow & x \color{blue}{-15x }
& = & 10 \color{blue}{+9} \\\Leftrightarrow &-14x
& = &19\\\Leftrightarrow & \color{red}{-14}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3-x }
& = & -11 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -11 \color{blue}{-3} \\\Leftrightarrow &-14x
& = &-14\\\Leftrightarrow & \color{red}{-14}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-14}{-14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+14}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-11x }
& = & 12 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & 12 \color{blue}{-14} \\\Leftrightarrow &-5x
& = &-2\\\Leftrightarrow & \color{red}{-5}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+12}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-13x }
& = & 15 \color{red}{ +13x }\color{blue}{-12-13x } \\\Leftrightarrow & -4x \color{blue}{-13x }
& = & 15 \color{blue}{-12} \\\Leftrightarrow &-17x
& = &3\\\Leftrightarrow & \color{red}{-17}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-x }
& = & 10 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & 10 \color{blue}{+4} \\\Leftrightarrow &13x
& = &14\\\Leftrightarrow & \color{red}{13}x
& = &14\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{14}{13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-8}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x }
& = & -9 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -9 \color{blue}{+8} \\\Leftrightarrow &-3x
& = &-1\\\Leftrightarrow & \color{red}{-3}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5-x }
& = & -9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -9 \color{blue}{-5} \\\Leftrightarrow &-9x
& = &-14\\\Leftrightarrow & \color{red}{-9}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-x }
& = & -8 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -8 \color{blue}{-6} \\\Leftrightarrow &-13x
& = &-14\\\Leftrightarrow & \color{red}{-13}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-12}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-x }
& = & 12 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 12 \color{blue}{+12} \\\Leftrightarrow &-14x
& = &24\\\Leftrightarrow & \color{red}{-14}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+11}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11-7x }
& = & 7 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -x \color{blue}{-7x }
& = & 7 \color{blue}{-11} \\\Leftrightarrow &-8x
& = &-4\\\Leftrightarrow & \color{red}{-8}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+7}& = & 11 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7+6x }
& = & 11 \color{red}{ -6x }\color{blue}{-7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & 11 \color{blue}{-7} \\\Leftrightarrow &19x
& = &4\\\Leftrightarrow & \color{red}{19}x
& = &4\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{4}{19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+3}\color{blue}{-3-x }
& = & 3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 3 \color{blue}{-3} \\\Leftrightarrow &x
& = &0\\\Leftrightarrow & \color{red}{}x
& = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)