Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-2x-7=-10+9x\)
- \(-3x+5=-5+10x\)
- \(-5x-5=13+x\)
- \(2x+6=-1+x\)
- \(-12x+11=9+x\)
- \(-14x+5=3+x\)
- \(-8x-10=12+x\)
- \(-3x+8=8+7x\)
- \(-x-3=3+3x\)
- \(10x-13=-10+7x\)
- \(-4x-13=14+x\)
- \(10x-11=11-13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -2x \color{red}{-7}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{-7}\color{blue}{+7-9x }
& = & -10 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -2x \color{blue}{-9x }
& = & -10 \color{blue}{+7} \\\Leftrightarrow &-11x
& = &-3\\\Leftrightarrow & \color{red}{-11}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+5}& = & -5 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-10x }
& = & -5 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & -3x \color{blue}{-10x }
& = & -5 \color{blue}{-5} \\\Leftrightarrow &-13x
& = &-10\\\Leftrightarrow & \color{red}{-13}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x }
& = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 13 \color{blue}{+5} \\\Leftrightarrow &-6x
& = &18\\\Leftrightarrow & \color{red}{-6}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{18}{-6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6-x }
& = & -1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -1 \color{blue}{-6} \\\Leftrightarrow &x
& = &-7\\\Leftrightarrow & \color{red}{}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11-x }
& = & 9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 9 \color{blue}{-11} \\\Leftrightarrow &-13x
& = &-2\\\Leftrightarrow & \color{red}{-13}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+5}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x }
& = & 3 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 3 \color{blue}{-5} \\\Leftrightarrow &-15x
& = &-2\\\Leftrightarrow & \color{red}{-15}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-10}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x }
& = & 12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 12 \color{blue}{+10} \\\Leftrightarrow &-9x
& = &22\\\Leftrightarrow & \color{red}{-9}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+8}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+8}\color{blue}{-8-7x }
& = & 8 \color{red}{ +7x }\color{blue}{-8-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & 8 \color{blue}{-8} \\\Leftrightarrow &-10x
& = &0\\\Leftrightarrow & \color{red}{-10}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-3}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-3x }
& = & 3 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & -x \color{blue}{-3x }
& = & 3 \color{blue}{+3} \\\Leftrightarrow &-4x
& = &6\\\Leftrightarrow & \color{red}{-4}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-13}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-7x }
& = & -10 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & -10 \color{blue}{+13} \\\Leftrightarrow &3x
& = &3\\\Leftrightarrow & \color{red}{3}x
& = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x }
& = & 14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 14 \color{blue}{+13} \\\Leftrightarrow &-5x
& = &27\\\Leftrightarrow & \color{red}{-5}x
& = &27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-11}& = & 11 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11+13x }
& = & 11 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & 10x \color{blue}{+13x }
& = & 11 \color{blue}{+11} \\\Leftrightarrow &23x
& = &22\\\Leftrightarrow & \color{red}{23}x
& = &22\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{22}{23} \\\Leftrightarrow & \color{green}{ x = \frac{22}{23} } & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)