Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-10x-11=11+x\)
- \(15x-13=15-14x\)
- \(12x+1=-12-11x\)
- \(-5x-10=-12+x\)
- \(x+6=11+6x\)
- \(4x+5=11-15x\)
- \(9x+13=14-4x\)
- \(-10x-1=12+11x\)
- \(10x-13=14+13x\)
- \(x+5=15+14x\)
- \(3x+14=-15+4x\)
- \(3x+10=-12+10x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -10x \color{red}{-11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x }
& = & 11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 11 \color{blue}{+11} \\\Leftrightarrow &-11x
& = &22\\\Leftrightarrow & \color{red}{-11}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{22}{-11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-13}& = & 15 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13+14x }
& = & 15 \color{red}{ -14x }\color{blue}{+13+14x } \\\Leftrightarrow & 15x \color{blue}{+14x }
& = & 15 \color{blue}{+13} \\\Leftrightarrow &29x
& = &28\\\Leftrightarrow & \color{red}{29}x
& = &28\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}}
& = & \frac{28}{29} \\\Leftrightarrow & \color{green}{ x = \frac{28}{29} } & & \\ & V = \left\{ \frac{28}{29} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+1}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1+11x }
& = & -12 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -12 \color{blue}{-1} \\\Leftrightarrow &23x
& = &-13\\\Leftrightarrow & \color{red}{23}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-x }
& = & -12 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -12 \color{blue}{+10} \\\Leftrightarrow &-6x
& = &-2\\\Leftrightarrow & \color{red}{-6}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+6}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6-6x }
& = & 11 \color{red}{ +6x }\color{blue}{-6-6x } \\\Leftrightarrow & x \color{blue}{-6x }
& = & 11 \color{blue}{-6} \\\Leftrightarrow &-5x
& = &5\\\Leftrightarrow & \color{red}{-5}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+5}& = & 11 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+15x }
& = & 11 \color{red}{ -15x }\color{blue}{-5+15x } \\\Leftrightarrow & 4x \color{blue}{+15x }
& = & 11 \color{blue}{-5} \\\Leftrightarrow &19x
& = &6\\\Leftrightarrow & \color{red}{19}x
& = &6\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{6}{19} \\\Leftrightarrow & \color{green}{ x = \frac{6}{19} } & & \\ & V = \left\{ \frac{6}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+13}& = & 14 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+4x }
& = & 14 \color{red}{ -4x }\color{blue}{-13+4x } \\\Leftrightarrow & 9x \color{blue}{+4x }
& = & 14 \color{blue}{-13} \\\Leftrightarrow &13x
& = &1\\\Leftrightarrow & \color{red}{13}x
& = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-1}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-11x }
& = & 12 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & -10x \color{blue}{-11x }
& = & 12 \color{blue}{+1} \\\Leftrightarrow &-21x
& = &13\\\Leftrightarrow & \color{red}{-21}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}}
& = & \frac{13}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{21} } & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-13}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-13x }
& = & 14 \color{red}{ +13x }\color{blue}{+13-13x } \\\Leftrightarrow & 10x \color{blue}{-13x }
& = & 14 \color{blue}{+13} \\\Leftrightarrow &-3x
& = &27\\\Leftrightarrow & \color{red}{-3}x
& = &27\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{27}{-3} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+5}& = & 15 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{+5}\color{blue}{-5-14x }
& = & 15 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & x \color{blue}{-14x }
& = & 15 \color{blue}{-5} \\\Leftrightarrow &-13x
& = &10\\\Leftrightarrow & \color{red}{-13}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+14}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-4x }
& = & -15 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & 3x \color{blue}{-4x }
& = & -15 \color{blue}{-14} \\\Leftrightarrow &-x
& = &-29\\\Leftrightarrow & \color{red}{-}x
& = &-29\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-29}{-1} \\\Leftrightarrow & \color{green}{ x = 29 } & & \\ & V = \left\{ 29 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+10}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-10x }
& = & -12 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & 3x \color{blue}{-10x }
& = & -12 \color{blue}{-10} \\\Leftrightarrow &-7x
& = &-22\\\Leftrightarrow & \color{red}{-7}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{22}{7} } & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)