Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(x-4=14+0x\)
- \(9x-8=-7+10x\)
- \(-2x+8=-8+5x\)
- \(15x-12=14-2x\)
- \(7x-2=8-2x\)
- \(-6x-12=-4+13x\)
- \(-5x+13=1+3x\)
- \(11x-6=-15-13x\)
- \(x+11=8-8x\)
- \(-9x-11=-2+14x\)
- \(7x-6=-13-3x\)
- \(11x-7=-7-2x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & x \color{red}{-4}& = & 14 \color{red}{ +0x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+0x }
& = & 14 \color{red}{ +0x }\color{blue}{+4+0x } \\\Leftrightarrow & x \color{blue}{+0x }
& = & 14 \color{blue}{+4} \\\Leftrightarrow &x
& = &18\\\Leftrightarrow & \color{red}{}x
& = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-8}& = & -7 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8-10x }
& = & -7 \color{red}{ +10x }\color{blue}{+8-10x } \\\Leftrightarrow & 9x \color{blue}{-10x }
& = & -7 \color{blue}{+8} \\\Leftrightarrow &-x
& = &1\\\Leftrightarrow & \color{red}{-}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+8}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-5x }
& = & -8 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -2x \color{blue}{-5x }
& = & -8 \color{blue}{-8} \\\Leftrightarrow &-7x
& = &-16\\\Leftrightarrow & \color{red}{-7}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-16}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-12}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+2x }
& = & 14 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & 14 \color{blue}{+12} \\\Leftrightarrow &17x
& = &26\\\Leftrightarrow & \color{red}{17}x
& = &26\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{26}{17} \\\Leftrightarrow & \color{green}{ x = \frac{26}{17} } & & \\ & V = \left\{ \frac{26}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-2}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2+2x }
& = & 8 \color{red}{ -2x }\color{blue}{+2+2x } \\\Leftrightarrow & 7x \color{blue}{+2x }
& = & 8 \color{blue}{+2} \\\Leftrightarrow &9x
& = &10\\\Leftrightarrow & \color{red}{9}x
& = &10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{10}{9} } & & \\ & V = \left\{ \frac{10}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-12}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x }
& = & -4 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -4 \color{blue}{+12} \\\Leftrightarrow &-19x
& = &8\\\Leftrightarrow & \color{red}{-19}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{8}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{19} } & & \\ & V = \left\{ \frac{-8}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+13}& = & 1 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-3x }
& = & 1 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & -5x \color{blue}{-3x }
& = & 1 \color{blue}{-13} \\\Leftrightarrow &-8x
& = &-12\\\Leftrightarrow & \color{red}{-8}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-6}& = & -15 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+13x }
& = & -15 \color{red}{ -13x }\color{blue}{+6+13x } \\\Leftrightarrow & 11x \color{blue}{+13x }
& = & -15 \color{blue}{+6} \\\Leftrightarrow &24x
& = &-9\\\Leftrightarrow & \color{red}{24}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}}
& = & \frac{-9}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+11}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11+8x }
& = & 8 \color{red}{ -8x }\color{blue}{-11+8x } \\\Leftrightarrow & x \color{blue}{+8x }
& = & 8 \color{blue}{-11} \\\Leftrightarrow &9x
& = &-3\\\Leftrightarrow & \color{red}{9}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-11}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-14x }
& = & -2 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & -2 \color{blue}{+11} \\\Leftrightarrow &-23x
& = &9\\\Leftrightarrow & \color{red}{-23}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{23} } & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-6}& = & -13 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6+3x }
& = & -13 \color{red}{ -3x }\color{blue}{+6+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & -13 \color{blue}{+6} \\\Leftrightarrow &10x
& = &-7\\\Leftrightarrow & \color{red}{10}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-7}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-7}& = & -7 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7+2x }
& = & -7 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 11x \color{blue}{+2x }
& = & -7 \color{blue}{+7} \\\Leftrightarrow &13x
& = &0\\\Leftrightarrow & \color{red}{13}x
& = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)