Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(15x-15=6-11x\)
- \(-x-7=-9+x\)
- \(-9x+10=-9+5x\)
- \(-7x-8=7+x\)
- \(12x+14=-12+13x\)
- \(-7x-11=-1+x\)
- \(12x+14=-1+7x\)
- \(-5x-15=-2+8x\)
- \(6x+9=15-5x\)
- \(13x+15=-9+12x\)
- \(-2x+13=-2+11x\)
- \(9x-2=3-8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 15x \color{red}{-15}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-15}\color{blue}{+15+11x }
& = & 6 \color{red}{ -11x }\color{blue}{+15+11x } \\\Leftrightarrow & 15x \color{blue}{+11x }
& = & 6 \color{blue}{+15} \\\Leftrightarrow &26x
& = &21\\\Leftrightarrow & \color{red}{26}x
& = &21\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}}
& = & \frac{21}{26} \\\Leftrightarrow & \color{green}{ x = \frac{21}{26} } & & \\ & V = \left\{ \frac{21}{26} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-7}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-x }
& = & -9 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -x \color{blue}{-x }
& = & -9 \color{blue}{+7} \\\Leftrightarrow &-2x
& = &-2\\\Leftrightarrow & \color{red}{-2}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{-2}{-2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+10}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+10}\color{blue}{-10-5x }
& = & -9 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & -9x \color{blue}{-5x }
& = & -9 \color{blue}{-10} \\\Leftrightarrow &-14x
& = &-19\\\Leftrightarrow & \color{red}{-14}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\ & V = \left\{ \frac{19}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x }
& = & 7 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 7 \color{blue}{+8} \\\Leftrightarrow &-8x
& = &15\\\Leftrightarrow & \color{red}{-8}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+14}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-13x }
& = & -12 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 12x \color{blue}{-13x }
& = & -12 \color{blue}{-14} \\\Leftrightarrow &-x
& = &-26\\\Leftrightarrow & \color{red}{-}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-26}{-1} \\\Leftrightarrow & \color{green}{ x = 26 } & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x }
& = & -1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -1 \color{blue}{+11} \\\Leftrightarrow &-8x
& = &10\\\Leftrightarrow & \color{red}{-8}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+14}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14-7x }
& = & -1 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 12x \color{blue}{-7x }
& = & -1 \color{blue}{-14} \\\Leftrightarrow &5x
& = &-15\\\Leftrightarrow & \color{red}{5}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-15}& = & -2 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-8x }
& = & -2 \color{red}{ +8x }\color{blue}{+15-8x } \\\Leftrightarrow & -5x \color{blue}{-8x }
& = & -2 \color{blue}{+15} \\\Leftrightarrow &-13x
& = &13\\\Leftrightarrow & \color{red}{-13}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{13}{-13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+9}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+5x }
& = & 15 \color{red}{ -5x }\color{blue}{-9+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & 15 \color{blue}{-9} \\\Leftrightarrow &11x
& = &6\\\Leftrightarrow & \color{red}{11}x
& = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+15}& = & -9 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-12x }
& = & -9 \color{red}{ +12x }\color{blue}{-15-12x } \\\Leftrightarrow & 13x \color{blue}{-12x }
& = & -9 \color{blue}{-15} \\\Leftrightarrow &x
& = &-24\\\Leftrightarrow & \color{red}{}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -24 \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+13}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13-11x }
& = & -2 \color{red}{ +11x }\color{blue}{-13-11x } \\\Leftrightarrow & -2x \color{blue}{-11x }
& = & -2 \color{blue}{-13} \\\Leftrightarrow &-13x
& = &-15\\\Leftrightarrow & \color{red}{-13}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-2}& = & 3 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+8x }
& = & 3 \color{red}{ -8x }\color{blue}{+2+8x } \\\Leftrightarrow & 9x \color{blue}{+8x }
& = & 3 \color{blue}{+2} \\\Leftrightarrow &17x
& = &5\\\Leftrightarrow & \color{red}{17}x
& = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)