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