Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-x-5=-5+3x\)
- \(2x+12=15+x\)
- \(-8x+2=-4+x\)
- \(-5x-10=-9+6x\)
- \(6x+9=-8+5x\)
- \(3x-1=2-14x\)
- \(11x-3=-3+7x\)
- \(13x-12=-11-12x\)
- \(-14x-11=-5+3x\)
- \(-5x-9=-3+x\)
- \(-6x-11=-7+7x\)
- \(12x+1=13+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -x \color{red}{-5}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-3x }
& = & -5 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & -x \color{blue}{-3x }
& = & -5 \color{blue}{+5} \\\Leftrightarrow &-4x
& = &0\\\Leftrightarrow & \color{red}{-4}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12-x }
& = & 15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 15 \color{blue}{-12} \\\Leftrightarrow &x
& = &3\\\Leftrightarrow & \color{red}{}x
& = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-x }
& = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -4 \color{blue}{-2} \\\Leftrightarrow &-9x
& = &-6\\\Leftrightarrow & \color{red}{-9}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-10}& = & -9 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10-6x }
& = & -9 \color{red}{ +6x }\color{blue}{+10-6x } \\\Leftrightarrow & -5x \color{blue}{-6x }
& = & -9 \color{blue}{+10} \\\Leftrightarrow &-11x
& = &1\\\Leftrightarrow & \color{red}{-11}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+9}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-5x }
& = & -8 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & 6x \color{blue}{-5x }
& = & -8 \color{blue}{-9} \\\Leftrightarrow &x
& = &-17\\\Leftrightarrow & \color{red}{}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-1}& = & 2 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+14x }
& = & 2 \color{red}{ -14x }\color{blue}{+1+14x } \\\Leftrightarrow & 3x \color{blue}{+14x }
& = & 2 \color{blue}{+1} \\\Leftrightarrow &17x
& = &3\\\Leftrightarrow & \color{red}{17}x
& = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-3}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3-7x }
& = & -3 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 11x \color{blue}{-7x }
& = & -3 \color{blue}{+3} \\\Leftrightarrow &4x
& = &0\\\Leftrightarrow & \color{red}{4}x
& = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-12}& = & -11 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-12}\color{blue}{+12+12x }
& = & -11 \color{red}{ -12x }\color{blue}{+12+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & -11 \color{blue}{+12} \\\Leftrightarrow &25x
& = &1\\\Leftrightarrow & \color{red}{25}x
& = &1\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{1}{25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{25} } & & \\ & V = \left\{ \frac{1}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-11}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-3x }
& = & -5 \color{red}{ +3x }\color{blue}{+11-3x } \\\Leftrightarrow & -14x \color{blue}{-3x }
& = & -5 \color{blue}{+11} \\\Leftrightarrow &-17x
& = &6\\\Leftrightarrow & \color{red}{-17}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{6}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{17} } & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-x }
& = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -3 \color{blue}{+9} \\\Leftrightarrow &-6x
& = &6\\\Leftrightarrow & \color{red}{-6}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-11}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-7x }
& = & -7 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -7 \color{blue}{+11} \\\Leftrightarrow &-13x
& = &4\\\Leftrightarrow & \color{red}{-13}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+1}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1-11x }
& = & 13 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 12x \color{blue}{-11x }
& = & 13 \color{blue}{-1} \\\Leftrightarrow &x
& = &12\\\Leftrightarrow & \color{red}{}x
& = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)