Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(6x+1=-12-5x\)
- \(-12x+3=3+x\)
- \(10x-3=10+3x\)
- \(10x+6=5+11x\)
- \(-11x-13=4+9x\)
- \(-9x-15=-14+x\)
- \(14x-1=-1+x\)
- \(-8x+4=2+x\)
- \(11x-14=-13-5x\)
- \(-15x+2=-13+13x\)
- \(11x-13=-3+12x\)
- \(4x+6=-1-7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 6x \color{red}{+1}& = & -12 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+1}\color{blue}{-1+5x }
& = & -12 \color{red}{ -5x }\color{blue}{-1+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & -12 \color{blue}{-1} \\\Leftrightarrow &11x
& = &-13\\\Leftrightarrow & \color{red}{11}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3-x }
& = & 3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 3 \color{blue}{-3} \\\Leftrightarrow &-13x
& = &0\\\Leftrightarrow & \color{red}{-13}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-3}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-3x }
& = & 10 \color{red}{ +3x }\color{blue}{+3-3x } \\\Leftrightarrow & 10x \color{blue}{-3x }
& = & 10 \color{blue}{+3} \\\Leftrightarrow &7x
& = &13\\\Leftrightarrow & \color{red}{7}x
& = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+6}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6-11x }
& = & 5 \color{red}{ +11x }\color{blue}{-6-11x } \\\Leftrightarrow & 10x \color{blue}{-11x }
& = & 5 \color{blue}{-6} \\\Leftrightarrow &-x
& = &-1\\\Leftrightarrow & \color{red}{-}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-13}& = & 4 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-9x }
& = & 4 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -11x \color{blue}{-9x }
& = & 4 \color{blue}{+13} \\\Leftrightarrow &-20x
& = &17\\\Leftrightarrow & \color{red}{-20}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{17}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{20} } & & \\ & V = \left\{ \frac{-17}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-15}\color{blue}{+15-x }
& = & -14 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -14 \color{blue}{+15} \\\Leftrightarrow &-10x
& = &1\\\Leftrightarrow & \color{red}{-10}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1-x }
& = & -1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -1 \color{blue}{+1} \\\Leftrightarrow &13x
& = &0\\\Leftrightarrow & \color{red}{13}x
& = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+4}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x }
& = & 2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 2 \color{blue}{-4} \\\Leftrightarrow &-9x
& = &-2\\\Leftrightarrow & \color{red}{-9}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-14}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14+5x }
& = & -13 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 11x \color{blue}{+5x }
& = & -13 \color{blue}{+14} \\\Leftrightarrow &16x
& = &1\\\Leftrightarrow & \color{red}{16}x
& = &1\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{1}{16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{16} } & & \\ & V = \left\{ \frac{1}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+2}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2-13x }
& = & -13 \color{red}{ +13x }\color{blue}{-2-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -13 \color{blue}{-2} \\\Leftrightarrow &-28x
& = &-15\\\Leftrightarrow & \color{red}{-28}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-15}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{15}{28} } & & \\ & V = \left\{ \frac{15}{28} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-13}& = & -3 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13-12x }
& = & -3 \color{red}{ +12x }\color{blue}{+13-12x } \\\Leftrightarrow & 11x \color{blue}{-12x }
& = & -3 \color{blue}{+13} \\\Leftrightarrow &-x
& = &10\\\Leftrightarrow & \color{red}{-}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+6}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+6}\color{blue}{-6+7x }
& = & -1 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & -1 \color{blue}{-6} \\\Leftrightarrow &11x
& = &-7\\\Leftrightarrow & \color{red}{11}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)