Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(12x-8=-1+5x\)
- \(-9x-14=3+x\)
- \(-15x+13=-12+x\)
- \(-x-10=10-7x\)
- \(-15x+1=2+13x\)
- \(7x+8=-14+10x\)
- \(8x-3=9-7x\)
- \(-10x-12=2+x\)
- \(-x+2=-1-2x\)
- \(-10x-14=-8+x\)
- \(13x-8=6+12x\)
- \(14x-6=3+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 12x \color{red}{-8}& = & -1 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-5x }
& = & -1 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 12x \color{blue}{-5x }
& = & -1 \color{blue}{+8} \\\Leftrightarrow &7x
& = &7\\\Leftrightarrow & \color{red}{7}x
& = &7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{7}{7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-14}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x }
& = & 3 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 3 \color{blue}{+14} \\\Leftrightarrow &-10x
& = &17\\\Leftrightarrow & \color{red}{-10}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{17}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+13}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+13}\color{blue}{-13-x }
& = & -12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -12 \color{blue}{-13} \\\Leftrightarrow &-16x
& = &-25\\\Leftrightarrow & \color{red}{-16}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-25}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{25}{16} } & & \\ & V = \left\{ \frac{25}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-10}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10+7x }
& = & 10 \color{red}{ -7x }\color{blue}{+10+7x } \\\Leftrightarrow & -x \color{blue}{+7x }
& = & 10 \color{blue}{+10} \\\Leftrightarrow &6x
& = &20\\\Leftrightarrow & \color{red}{6}x
& = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+1}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+1}\color{blue}{-1-13x }
& = & 2 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & 2 \color{blue}{-1} \\\Leftrightarrow &-28x
& = &1\\\Leftrightarrow & \color{red}{-28}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{1}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{28} } & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+8}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-10x }
& = & -14 \color{red}{ +10x }\color{blue}{-8-10x } \\\Leftrightarrow & 7x \color{blue}{-10x }
& = & -14 \color{blue}{-8} \\\Leftrightarrow &-3x
& = &-22\\\Leftrightarrow & \color{red}{-3}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-3}& = & 9 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3+7x }
& = & 9 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & 9 \color{blue}{+3} \\\Leftrightarrow &15x
& = &12\\\Leftrightarrow & \color{red}{15}x
& = &12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-12}\color{blue}{+12-x }
& = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 2 \color{blue}{+12} \\\Leftrightarrow &-11x
& = &14\\\Leftrightarrow & \color{red}{-11}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+2}& = & -1 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+2}\color{blue}{-2+2x }
& = & -1 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & -x \color{blue}{+2x }
& = & -1 \color{blue}{-2} \\\Leftrightarrow &x
& = &-3\\\Leftrightarrow & \color{red}{}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14-x }
& = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -8 \color{blue}{+14} \\\Leftrightarrow &-11x
& = &6\\\Leftrightarrow & \color{red}{-11}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-8}& = & 6 \color{red}{ +12x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8-12x }
& = & 6 \color{red}{ +12x }\color{blue}{+8-12x } \\\Leftrightarrow & 13x \color{blue}{-12x }
& = & 6 \color{blue}{+8} \\\Leftrightarrow &x
& = &14\\\Leftrightarrow & \color{red}{}x
& = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6-x }
& = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & 3 \color{blue}{+6} \\\Leftrightarrow &13x
& = &9\\\Leftrightarrow & \color{red}{13}x
& = &9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)