Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(8x+7=8+x\)
- \(-12x+4=-8+x\)
- \(-12x-12=9+5x\)
- \(-12x+8=3+13x\)
- \(15x+7=12+14x\)
- \(-12x-4=-3+x\)
- \(-3x+11=12+13x\)
- \(-5x+6=-6+6x\)
- \(3x-14=7-11x\)
- \(-6x+7=-9+13x\)
- \(-9x-3=-9+x\)
- \(-7x-3=7+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 8x \color{red}{+7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7-x }
& = & 8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & 8 \color{blue}{-7} \\\Leftrightarrow &7x
& = &1\\\Leftrightarrow & \color{red}{7}x
& = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x }
& = & -8 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -8 \color{blue}{-4} \\\Leftrightarrow &-13x
& = &-12\\\Leftrightarrow & \color{red}{-13}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-12}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-5x }
& = & 9 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -12x \color{blue}{-5x }
& = & 9 \color{blue}{+12} \\\Leftrightarrow &-17x
& = &21\\\Leftrightarrow & \color{red}{-17}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+8}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-13x }
& = & 3 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 3 \color{blue}{-8} \\\Leftrightarrow &-25x
& = &-5\\\Leftrightarrow & \color{red}{-25}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+7}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7-14x }
& = & 12 \color{red}{ +14x }\color{blue}{-7-14x } \\\Leftrightarrow & 15x \color{blue}{-14x }
& = & 12 \color{blue}{-7} \\\Leftrightarrow &x
& = &5\\\Leftrightarrow & \color{red}{}x
& = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-4}\color{blue}{+4-x }
& = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -3 \color{blue}{+4} \\\Leftrightarrow &-13x
& = &1\\\Leftrightarrow & \color{red}{-13}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+11}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-13x }
& = & 12 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -3x \color{blue}{-13x }
& = & 12 \color{blue}{-11} \\\Leftrightarrow &-16x
& = &1\\\Leftrightarrow & \color{red}{-16}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+6}& = & -6 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-6x }
& = & -6 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & -5x \color{blue}{-6x }
& = & -6 \color{blue}{-6} \\\Leftrightarrow &-11x
& = &-12\\\Leftrightarrow & \color{red}{-11}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-14}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+11x }
& = & 7 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 3x \color{blue}{+11x }
& = & 7 \color{blue}{+14} \\\Leftrightarrow &14x
& = &21\\\Leftrightarrow & \color{red}{14}x
& = &21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+7}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7-13x }
& = & -9 \color{red}{ +13x }\color{blue}{-7-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -9 \color{blue}{-7} \\\Leftrightarrow &-19x
& = &-16\\\Leftrightarrow & \color{red}{-19}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x }
& = & -9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -9 \color{blue}{+3} \\\Leftrightarrow &-10x
& = &-6\\\Leftrightarrow & \color{red}{-10}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-x }
& = & 7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 7 \color{blue}{+3} \\\Leftrightarrow &-8x
& = &10\\\Leftrightarrow & \color{red}{-8}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)