Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x+11=2+10x\)
- \(-8x-3=-6+9x\)
- \(8x+14=-7-7x\)
- \(6x-1=-7-11x\)
- \(11x+11=10-7x\)
- \(9x-1=15+7x\)
- \(-4x+1=-10+x\)
- \(13x+2=-6+x\)
- \(-2x-12=-11+x\)
- \(8x-13=8+x\)
- \(-14x+3=-11+3x\)
- \(-5x-5=5+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{+11}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-10x }
& = & 2 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & -9x \color{blue}{-10x }
& = & 2 \color{blue}{-11} \\\Leftrightarrow &-19x
& = &-9\\\Leftrightarrow & \color{red}{-19}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-9}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{9}{19} } & & \\ & V = \left\{ \frac{9}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-3}& = & -6 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-9x }
& = & -6 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -6 \color{blue}{+3} \\\Leftrightarrow &-17x
& = &-3\\\Leftrightarrow & \color{red}{-17}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+14}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14+7x }
& = & -7 \color{red}{ -7x }\color{blue}{-14+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & -7 \color{blue}{-14} \\\Leftrightarrow &15x
& = &-21\\\Leftrightarrow & \color{red}{15}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{-21}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-1}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1+11x }
& = & -7 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & -7 \color{blue}{+1} \\\Leftrightarrow &17x
& = &-6\\\Leftrightarrow & \color{red}{17}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+11}& = & 10 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+7x }
& = & 10 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 11x \color{blue}{+7x }
& = & 10 \color{blue}{-11} \\\Leftrightarrow &18x
& = &-1\\\Leftrightarrow & \color{red}{18}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}}
& = & \frac{-1}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{18} } & & \\ & V = \left\{ \frac{-1}{18} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-1}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1-7x }
& = & 15 \color{red}{ +7x }\color{blue}{+1-7x } \\\Leftrightarrow & 9x \color{blue}{-7x }
& = & 15 \color{blue}{+1} \\\Leftrightarrow &2x
& = &16\\\Leftrightarrow & \color{red}{2}x
& = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+1}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x }
& = & -10 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -10 \color{blue}{-1} \\\Leftrightarrow &-5x
& = &-11\\\Leftrightarrow & \color{red}{-5}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{11}{5} } & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+2}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2-x }
& = & -6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 13x \color{blue}{-x }
& = & -6 \color{blue}{-2} \\\Leftrightarrow &12x
& = &-8\\\Leftrightarrow & \color{red}{12}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-8}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-12}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x }
& = & -11 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -11 \color{blue}{+12} \\\Leftrightarrow &-3x
& = &1\\\Leftrightarrow & \color{red}{-3}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-x }
& = & 8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & 8 \color{blue}{+13} \\\Leftrightarrow &7x
& = &21\\\Leftrightarrow & \color{red}{7}x
& = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+3}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3-3x }
& = & -11 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & -14x \color{blue}{-3x }
& = & -11 \color{blue}{-3} \\\Leftrightarrow &-17x
& = &-14\\\Leftrightarrow & \color{red}{-17}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-14}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-5}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x }
& = & 5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 5 \color{blue}{+5} \\\Leftrightarrow &-6x
& = &10\\\Leftrightarrow & \color{red}{-6}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)