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