Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-2x-9=9+x\)
- \(12x+13=-9-11x\)
- \(6x+8=8-11x\)
- \(-9x+9=-14+14x\)
- \(-2x-12=-3+x\)
- \(-3x-1=15+13x\)
- \(-13x+7=-12+x\)
- \(13x-1=-11-6x\)
- \(-5x+3=-3+3x\)
- \(-15x-13=10+x\)
- \(14x-15=-2+x\)
- \(-10x-6=8+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -2x \color{red}{-9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9-x }
& = & 9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 9 \color{blue}{+9} \\\Leftrightarrow &-3x
& = &18\\\Leftrightarrow & \color{red}{-3}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+13}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13+11x }
& = & -9 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -9 \color{blue}{-13} \\\Leftrightarrow &23x
& = &-22\\\Leftrightarrow & \color{red}{23}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-22}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{23} } & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+8}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+11x }
& = & 8 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 8 \color{blue}{-8} \\\Leftrightarrow &17x
& = &0\\\Leftrightarrow & \color{red}{17}x
& = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+9}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-14x }
& = & -14 \color{red}{ +14x }\color{blue}{-9-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & -14 \color{blue}{-9} \\\Leftrightarrow &-23x
& = &-23\\\Leftrightarrow & \color{red}{-23}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-23}{-23} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-12}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x }
& = & -3 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -3 \color{blue}{+12} \\\Leftrightarrow &-3x
& = &9\\\Leftrightarrow & \color{red}{-3}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{9}{-3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-1}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-13x }
& = & 15 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & -3x \color{blue}{-13x }
& = & 15 \color{blue}{+1} \\\Leftrightarrow &-16x
& = &16\\\Leftrightarrow & \color{red}{-16}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{16}{-16} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7-x }
& = & -12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -12 \color{blue}{-7} \\\Leftrightarrow &-14x
& = &-19\\\Leftrightarrow & \color{red}{-14}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-1}& = & -11 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1+6x }
& = & -11 \color{red}{ -6x }\color{blue}{+1+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & -11 \color{blue}{+1} \\\Leftrightarrow &19x
& = &-10\\\Leftrightarrow & \color{red}{19}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+3}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-3x }
& = & -3 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & -3 \color{blue}{-3} \\\Leftrightarrow &-8x
& = &-6\\\Leftrightarrow & \color{red}{-8}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13-x }
& = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 10 \color{blue}{+13} \\\Leftrightarrow &-16x
& = &23\\\Leftrightarrow & \color{red}{-16}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{16} } & & \\ & V = \left\{ \frac{-23}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15-x }
& = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -2 \color{blue}{+15} \\\Leftrightarrow &13x
& = &13\\\Leftrightarrow & \color{red}{13}x
& = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x }
& = & 8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 8 \color{blue}{+6} \\\Leftrightarrow &-11x
& = &14\\\Leftrightarrow & \color{red}{-11}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)