Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-11x-5=9+14x\)
- \(-8x+1=-12+x\)
- \(x-9=-2+10x\)
- \(6x+1=-15+x\)
- \(-6x-10=-10+13x\)
- \(8x+4=-4+13x\)
- \(8x-6=-4+11x\)
- \(12x-9=8-11x\)
- \(12x-8=9+5x\)
- \(x+5=1-7x\)
- \(-13x-13=-3+x\)
- \(8x+14=14+3x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -11x \color{red}{-5}& = & 9 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5-14x }
& = & 9 \color{red}{ +14x }\color{blue}{+5-14x } \\\Leftrightarrow & -11x \color{blue}{-14x }
& = & 9 \color{blue}{+5} \\\Leftrightarrow &-25x
& = &14\\\Leftrightarrow & \color{red}{-25}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{14}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{25} } & & \\ & V = \left\{ \frac{-14}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+1}\color{blue}{-1-x }
& = & -12 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -12 \color{blue}{-1} \\\Leftrightarrow &-9x
& = &-13\\\Leftrightarrow & \color{red}{-9}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-9}& = & -2 \color{red}{ +10x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9-10x }
& = & -2 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & x \color{blue}{-10x }
& = & -2 \color{blue}{+9} \\\Leftrightarrow &-9x
& = &7\\\Leftrightarrow & \color{red}{-9}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1-x }
& = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -15 \color{blue}{-1} \\\Leftrightarrow &5x
& = &-16\\\Leftrightarrow & \color{red}{5}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-10}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10-13x }
& = & -10 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -10 \color{blue}{+10} \\\Leftrightarrow &-19x
& = &0\\\Leftrightarrow & \color{red}{-19}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+4}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-13x }
& = & -4 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & 8x \color{blue}{-13x }
& = & -4 \color{blue}{-4} \\\Leftrightarrow &-5x
& = &-8\\\Leftrightarrow & \color{red}{-5}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-6}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6-11x }
& = & -4 \color{red}{ +11x }\color{blue}{+6-11x } \\\Leftrightarrow & 8x \color{blue}{-11x }
& = & -4 \color{blue}{+6} \\\Leftrightarrow &-3x
& = &2\\\Leftrightarrow & \color{red}{-3}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-9}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+11x }
& = & 8 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 8 \color{blue}{+9} \\\Leftrightarrow &23x
& = &17\\\Leftrightarrow & \color{red}{23}x
& = &17\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{17}{23} \\\Leftrightarrow & \color{green}{ x = \frac{17}{23} } & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-8}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-5x }
& = & 9 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 12x \color{blue}{-5x }
& = & 9 \color{blue}{+8} \\\Leftrightarrow &7x
& = &17\\\Leftrightarrow & \color{red}{7}x
& = &17\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{17}{7} \\\Leftrightarrow & \color{green}{ x = \frac{17}{7} } & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+5}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5+7x }
& = & 1 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & x \color{blue}{+7x }
& = & 1 \color{blue}{-5} \\\Leftrightarrow &8x
& = &-4\\\Leftrightarrow & \color{red}{8}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-13}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x }
& = & -3 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -3 \color{blue}{+13} \\\Leftrightarrow &-14x
& = &10\\\Leftrightarrow & \color{red}{-14}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+14}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14-3x }
& = & 14 \color{red}{ +3x }\color{blue}{-14-3x } \\\Leftrightarrow & 8x \color{blue}{-3x }
& = & 14 \color{blue}{-14} \\\Leftrightarrow &5x
& = &0\\\Leftrightarrow & \color{red}{5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)