Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x+12=11+10x\)
- \(11x-11=8-10x\)
- \(-7x-10=-8+4x\)
- \(-13x-8=11+x\)
- \(12x+9=-3-11x\)
- \(-6x+6=6+13x\)
- \(-3x-10=14+7x\)
- \(5x+15=-15-7x\)
- \(14x+3=1+5x\)
- \(3x-2=9+5x\)
- \(-13x-8=-14+x\)
- \(-9x+13=-11+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{+12}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-10x }
& = & 11 \color{red}{ +10x }\color{blue}{-12-10x } \\\Leftrightarrow & -9x \color{blue}{-10x }
& = & 11 \color{blue}{-12} \\\Leftrightarrow &-19x
& = &-1\\\Leftrightarrow & \color{red}{-19}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-11}& = & 8 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11+10x }
& = & 8 \color{red}{ -10x }\color{blue}{+11+10x } \\\Leftrightarrow & 11x \color{blue}{+10x }
& = & 8 \color{blue}{+11} \\\Leftrightarrow &21x
& = &19\\\Leftrightarrow & \color{red}{21}x
& = &19\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{19}{21} \\\Leftrightarrow & \color{green}{ x = \frac{19}{21} } & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-10}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-4x }
& = & -8 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -7x \color{blue}{-4x }
& = & -8 \color{blue}{+10} \\\Leftrightarrow &-11x
& = &2\\\Leftrightarrow & \color{red}{-11}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x }
& = & 11 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 11 \color{blue}{+8} \\\Leftrightarrow &-14x
& = &19\\\Leftrightarrow & \color{red}{-14}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+9}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x }
& = & -3 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -3 \color{blue}{-9} \\\Leftrightarrow &23x
& = &-12\\\Leftrightarrow & \color{red}{23}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{23} } & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+6}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-13x }
& = & 6 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & 6 \color{blue}{-6} \\\Leftrightarrow &-19x
& = &0\\\Leftrightarrow & \color{red}{-19}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-10}& = & 14 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-7x }
& = & 14 \color{red}{ +7x }\color{blue}{+10-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & 14 \color{blue}{+10} \\\Leftrightarrow &-10x
& = &24\\\Leftrightarrow & \color{red}{-10}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+15}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15+7x }
& = & -15 \color{red}{ -7x }\color{blue}{-15+7x } \\\Leftrightarrow & 5x \color{blue}{+7x }
& = & -15 \color{blue}{-15} \\\Leftrightarrow &12x
& = &-30\\\Leftrightarrow & \color{red}{12}x
& = &-30\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-30}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+3}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-5x }
& = & 1 \color{red}{ +5x }\color{blue}{-3-5x } \\\Leftrightarrow & 14x \color{blue}{-5x }
& = & 1 \color{blue}{-3} \\\Leftrightarrow &9x
& = &-2\\\Leftrightarrow & \color{red}{9}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-2}& = & 9 \color{red}{ +5x } \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2-5x }
& = & 9 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 3x \color{blue}{-5x }
& = & 9 \color{blue}{+2} \\\Leftrightarrow &-2x
& = &11\\\Leftrightarrow & \color{red}{-2}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-x }
& = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -14 \color{blue}{+8} \\\Leftrightarrow &-14x
& = &-6\\\Leftrightarrow & \color{red}{-14}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x }
& = & -11 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -11 \color{blue}{-13} \\\Leftrightarrow &-10x
& = &-24\\\Leftrightarrow & \color{red}{-10}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)