Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-12x+3=-15+x\)
- \(-14x+1=-10+x\)
- \(15x-10=-1-2x\)
- \(7x+14=1-13x\)
- \(-9x+2=-8+14x\)
- \(8x+11=6+3x\)
- \(-8x+11=7+x\)
- \(15x-5=-15-2x\)
- \(-2x+9=9+x\)
- \(-4x-6=-3+5x\)
- \(-5x-6=-2+6x\)
- \(-14x-11=-8+3x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -12x \color{red}{+3}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x }
& = & -15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -15 \color{blue}{-3} \\\Leftrightarrow &-13x
& = &-18\\\Leftrightarrow & \color{red}{-13}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1-x }
& = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -10 \color{blue}{-1} \\\Leftrightarrow &-15x
& = &-11\\\Leftrightarrow & \color{red}{-15}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-11}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-10}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10+2x }
& = & -1 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & -1 \color{blue}{+10} \\\Leftrightarrow &17x
& = &9\\\Leftrightarrow & \color{red}{17}x
& = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+14}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14+13x }
& = & 1 \color{red}{ -13x }\color{blue}{-14+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & 1 \color{blue}{-14} \\\Leftrightarrow &20x
& = &-13\\\Leftrightarrow & \color{red}{20}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-13}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{20} } & & \\ & V = \left\{ \frac{-13}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+2}& = & -8 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-14x }
& = & -8 \color{red}{ +14x }\color{blue}{-2-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & -8 \color{blue}{-2} \\\Leftrightarrow &-23x
& = &-10\\\Leftrightarrow & \color{red}{-23}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+11}& = & 6 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-3x }
& = & 6 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & 8x \color{blue}{-3x }
& = & 6 \color{blue}{-11} \\\Leftrightarrow &5x
& = &-5\\\Leftrightarrow & \color{red}{5}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+11}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x }
& = & 7 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 7 \color{blue}{-11} \\\Leftrightarrow &-9x
& = &-4\\\Leftrightarrow & \color{red}{-9}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-5}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-5}\color{blue}{+5+2x }
& = & -15 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & -15 \color{blue}{+5} \\\Leftrightarrow &17x
& = &-10\\\Leftrightarrow & \color{red}{17}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-x }
& = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 9 \color{blue}{-9} \\\Leftrightarrow &-3x
& = &0\\\Leftrightarrow & \color{red}{-3}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-6}& = & -3 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-5x }
& = & -3 \color{red}{ +5x }\color{blue}{+6-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & -3 \color{blue}{+6} \\\Leftrightarrow &-9x
& = &3\\\Leftrightarrow & \color{red}{-9}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-6}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-6x }
& = & -2 \color{red}{ +6x }\color{blue}{+6-6x } \\\Leftrightarrow & -5x \color{blue}{-6x }
& = & -2 \color{blue}{+6} \\\Leftrightarrow &-11x
& = &4\\\Leftrightarrow & \color{red}{-11}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-11}& = & -8 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-3x }
& = & -8 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -14x \color{blue}{-3x }
& = & -8 \color{blue}{+11} \\\Leftrightarrow &-17x
& = &3\\\Leftrightarrow & \color{red}{-17}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)