Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(12x+13=-10+x\)
- \(8x+13=12-15x\)
- \(-11x-2=-9+6x\)
- \(2x+13=4+3x\)
- \(-4x-3=7+x\)
- \(-3x+2=3+10x\)
- \(12x+7=8+7x\)
- \(x+5=4+2x\)
- \(-x-13=15-11x\)
- \(-14x+14=7+x\)
- \(14x+13=7-11x\)
- \(-12x+14=15+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 12x \color{red}{+13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13-x }
& = & -10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -10 \color{blue}{-13} \\\Leftrightarrow &11x
& = &-23\\\Leftrightarrow & \color{red}{11}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-23}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+13}& = & 12 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13+15x }
& = & 12 \color{red}{ -15x }\color{blue}{-13+15x } \\\Leftrightarrow & 8x \color{blue}{+15x }
& = & 12 \color{blue}{-13} \\\Leftrightarrow &23x
& = &-1\\\Leftrightarrow & \color{red}{23}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-2}& = & -9 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-2}\color{blue}{+2-6x }
& = & -9 \color{red}{ +6x }\color{blue}{+2-6x } \\\Leftrightarrow & -11x \color{blue}{-6x }
& = & -9 \color{blue}{+2} \\\Leftrightarrow &-17x
& = &-7\\\Leftrightarrow & \color{red}{-17}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+13}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-3x }
& = & 4 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & 2x \color{blue}{-3x }
& = & 4 \color{blue}{-13} \\\Leftrightarrow &-x
& = &-9\\\Leftrightarrow & \color{red}{-}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-x }
& = & 7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 7 \color{blue}{+3} \\\Leftrightarrow &-5x
& = &10\\\Leftrightarrow & \color{red}{-5}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+2}& = & 3 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-10x }
& = & 3 \color{red}{ +10x }\color{blue}{-2-10x } \\\Leftrightarrow & -3x \color{blue}{-10x }
& = & 3 \color{blue}{-2} \\\Leftrightarrow &-13x
& = &1\\\Leftrightarrow & \color{red}{-13}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+7}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-7x }
& = & 8 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 12x \color{blue}{-7x }
& = & 8 \color{blue}{-7} \\\Leftrightarrow &5x
& = &1\\\Leftrightarrow & \color{red}{5}x
& = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+5}& = & 4 \color{red}{ +2x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-2x }
& = & 4 \color{red}{ +2x }\color{blue}{-5-2x } \\\Leftrightarrow & x \color{blue}{-2x }
& = & 4 \color{blue}{-5} \\\Leftrightarrow &-x
& = &-1\\\Leftrightarrow & \color{red}{-}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-13}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+11x }
& = & 15 \color{red}{ -11x }\color{blue}{+13+11x } \\\Leftrightarrow & -x \color{blue}{+11x }
& = & 15 \color{blue}{+13} \\\Leftrightarrow &10x
& = &28\\\Leftrightarrow & \color{red}{10}x
& = &28\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{28}{10} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+14}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14-x }
& = & 7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 7 \color{blue}{-14} \\\Leftrightarrow &-15x
& = &-7\\\Leftrightarrow & \color{red}{-15}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+13}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13+11x }
& = & 7 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 14x \color{blue}{+11x }
& = & 7 \color{blue}{-13} \\\Leftrightarrow &25x
& = &-6\\\Leftrightarrow & \color{red}{25}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-6}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{25} } & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+14}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14-13x }
& = & 15 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 15 \color{blue}{-14} \\\Leftrightarrow &-25x
& = &1\\\Leftrightarrow & \color{red}{-25}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{1}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{25} } & & \\ & V = \left\{ \frac{-1}{25} \right\} & \\\end{align}\)