Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(12x-6=2-11x\)
- \(3x+6=-1-2x\)
- \(-14x+12=7+x\)
- \(14x-7=15+x\)
- \(6x+3=-2+5x\)
- \(-6x-11=-1+x\)
- \(-9x-3=10+14x\)
- \(2x+1=-2+3x\)
- \(5x+8=7-12x\)
- \(-11x+14=3+9x\)
- \(-11x+10=-3+x\)
- \(-10x-2=-12+7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 12x \color{red}{-6}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6+11x }
& = & 2 \color{red}{ -11x }\color{blue}{+6+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 2 \color{blue}{+6} \\\Leftrightarrow &23x
& = &8\\\Leftrightarrow & \color{red}{23}x
& = &8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+6}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6+2x }
& = & -1 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & -1 \color{blue}{-6} \\\Leftrightarrow &5x
& = &-7\\\Leftrightarrow & \color{red}{5}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x }
& = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 7 \color{blue}{-12} \\\Leftrightarrow &-15x
& = &-5\\\Leftrightarrow & \color{red}{-15}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-x }
& = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & 15 \color{blue}{+7} \\\Leftrightarrow &13x
& = &22\\\Leftrightarrow & \color{red}{13}x
& = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+3}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-5x }
& = & -2 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 6x \color{blue}{-5x }
& = & -2 \color{blue}{-3} \\\Leftrightarrow &x
& = &-5\\\Leftrightarrow & \color{red}{}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-11}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-x }
& = & -1 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -1 \color{blue}{+11} \\\Leftrightarrow &-7x
& = &10\\\Leftrightarrow & \color{red}{-7}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-3}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-14x }
& = & 10 \color{red}{ +14x }\color{blue}{+3-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & 10 \color{blue}{+3} \\\Leftrightarrow &-23x
& = &13\\\Leftrightarrow & \color{red}{-23}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{13}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+1}& = & -2 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-3x }
& = & -2 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 2x \color{blue}{-3x }
& = & -2 \color{blue}{-1} \\\Leftrightarrow &-x
& = &-3\\\Leftrightarrow & \color{red}{-}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+8}& = & 7 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{+8}\color{blue}{-8+12x }
& = & 7 \color{red}{ -12x }\color{blue}{-8+12x } \\\Leftrightarrow & 5x \color{blue}{+12x }
& = & 7 \color{blue}{-8} \\\Leftrightarrow &17x
& = &-1\\\Leftrightarrow & \color{red}{17}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+14}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{+14}\color{blue}{-14-9x }
& = & 3 \color{red}{ +9x }\color{blue}{-14-9x } \\\Leftrightarrow & -11x \color{blue}{-9x }
& = & 3 \color{blue}{-14} \\\Leftrightarrow &-20x
& = &-11\\\Leftrightarrow & \color{red}{-20}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{-11}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{11}{20} } & & \\ & V = \left\{ \frac{11}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x }
& = & -3 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -3 \color{blue}{-10} \\\Leftrightarrow &-12x
& = &-13\\\Leftrightarrow & \color{red}{-12}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-2}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-7x }
& = & -12 \color{red}{ +7x }\color{blue}{+2-7x } \\\Leftrightarrow & -10x \color{blue}{-7x }
& = & -12 \color{blue}{+2} \\\Leftrightarrow &-17x
& = &-10\\\Leftrightarrow & \color{red}{-17}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)