Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-6x-3=15+x\)
- \(11x+12=10-2x\)
- \(-13x-15=14+11x\)
- \(-6x+13=-8+13x\)
- \(-14x-14=12+x\)
- \(2x+14=-11+11x\)
- \(-11x+7=6+x\)
- \(-14x+7=-1+x\)
- \(-6x+7=4+13x\)
- \(5x+11=-5-12x\)
- \(13x+15=-13+10x\)
- \(-14x+1=-5+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -6x \color{red}{-3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-x }
& = & 15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 15 \color{blue}{+3} \\\Leftrightarrow &-7x
& = &18\\\Leftrightarrow & \color{red}{-7}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+12}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12+2x }
& = & 10 \color{red}{ -2x }\color{blue}{-12+2x } \\\Leftrightarrow & 11x \color{blue}{+2x }
& = & 10 \color{blue}{-12} \\\Leftrightarrow &13x
& = &-2\\\Leftrightarrow & \color{red}{13}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-15}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-11x }
& = & 14 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -13x \color{blue}{-11x }
& = & 14 \color{blue}{+15} \\\Leftrightarrow &-24x
& = &29\\\Leftrightarrow & \color{red}{-24}x
& = &29\\\Leftrightarrow & \frac{\color{red}{-24}x}{ \color{blue}{ -24}}
& = & \frac{29}{-24} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{24} } & & \\ & V = \left\{ \frac{-29}{24} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+13}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-13x }
& = & -8 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -8 \color{blue}{-13} \\\Leftrightarrow &-19x
& = &-21\\\Leftrightarrow & \color{red}{-19}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x }
& = & 12 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 12 \color{blue}{+14} \\\Leftrightarrow &-15x
& = &26\\\Leftrightarrow & \color{red}{-15}x
& = &26\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{26}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{15} } & & \\ & V = \left\{ \frac{-26}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+14}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-11x }
& = & -11 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 2x \color{blue}{-11x }
& = & -11 \color{blue}{-14} \\\Leftrightarrow &-9x
& = &-25\\\Leftrightarrow & \color{red}{-9}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-25}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{25}{9} } & & \\ & V = \left\{ \frac{25}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+7}\color{blue}{-7-x }
& = & 6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 6 \color{blue}{-7} \\\Leftrightarrow &-12x
& = &-1\\\Leftrightarrow & \color{red}{-12}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{12} } & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+7}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x }
& = & -1 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -1 \color{blue}{-7} \\\Leftrightarrow &-15x
& = &-8\\\Leftrightarrow & \color{red}{-15}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+7}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-13x }
& = & 4 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & 4 \color{blue}{-7} \\\Leftrightarrow &-19x
& = &-3\\\Leftrightarrow & \color{red}{-19}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+11}& = & -5 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11+12x }
& = & -5 \color{red}{ -12x }\color{blue}{-11+12x } \\\Leftrightarrow & 5x \color{blue}{+12x }
& = & -5 \color{blue}{-11} \\\Leftrightarrow &17x
& = &-16\\\Leftrightarrow & \color{red}{17}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+15}& = & -13 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-10x }
& = & -13 \color{red}{ +10x }\color{blue}{-15-10x } \\\Leftrightarrow & 13x \color{blue}{-10x }
& = & -13 \color{blue}{-15} \\\Leftrightarrow &3x
& = &-28\\\Leftrightarrow & \color{red}{3}x
& = &-28\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-28}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{3} } & & \\ & V = \left\{ \frac{-28}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x }
& = & -5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -5 \color{blue}{-1} \\\Leftrightarrow &-15x
& = &-6\\\Leftrightarrow & \color{red}{-15}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)