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