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