Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x-12=9-11x\)
- \(-x-5=-2-9x\)
- \(12x-10=8+x\)
- \(6x-2=2+5x\)
- \(-x-11=4+7x\)
- \(12x-7=-7+11x\)
- \(7x+8=-11+12x\)
- \(12x-1=-10+13x\)
- \(-13x+4=3+x\)
- \(-9x-9=-11+14x\)
- \(2x-5=14+3x\)
- \(6x+4=-14+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{-12}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+11x }
& = & 9 \color{red}{ -11x }\color{blue}{+12+11x } \\\Leftrightarrow & 3x \color{blue}{+11x }
& = & 9 \color{blue}{+12} \\\Leftrightarrow &14x
& = &21\\\Leftrightarrow & \color{red}{14}x
& = &21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-5}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5+9x }
& = & -2 \color{red}{ -9x }\color{blue}{+5+9x } \\\Leftrightarrow & -x \color{blue}{+9x }
& = & -2 \color{blue}{+5} \\\Leftrightarrow &8x
& = &3\\\Leftrightarrow & \color{red}{8}x
& = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-x }
& = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 8 \color{blue}{+10} \\\Leftrightarrow &11x
& = &18\\\Leftrightarrow & \color{red}{11}x
& = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-2}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-5x }
& = & 2 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 6x \color{blue}{-5x }
& = & 2 \color{blue}{+2} \\\Leftrightarrow &x
& = &4\\\Leftrightarrow & \color{red}{}x
& = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-11}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11-7x }
& = & 4 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -x \color{blue}{-7x }
& = & 4 \color{blue}{+11} \\\Leftrightarrow &-8x
& = &15\\\Leftrightarrow & \color{red}{-8}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-7}& = & -7 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7-11x }
& = & -7 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 12x \color{blue}{-11x }
& = & -7 \color{blue}{+7} \\\Leftrightarrow &x
& = &0\\\Leftrightarrow & \color{red}{}x
& = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+8}& = & -11 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8-12x }
& = & -11 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & 7x \color{blue}{-12x }
& = & -11 \color{blue}{-8} \\\Leftrightarrow &-5x
& = &-19\\\Leftrightarrow & \color{red}{-5}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-1}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-13x }
& = & -10 \color{red}{ +13x }\color{blue}{+1-13x } \\\Leftrightarrow & 12x \color{blue}{-13x }
& = & -10 \color{blue}{+1} \\\Leftrightarrow &-x
& = &-9\\\Leftrightarrow & \color{red}{-}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+4}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x }
& = & 3 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 3 \color{blue}{-4} \\\Leftrightarrow &-14x
& = &-1\\\Leftrightarrow & \color{red}{-14}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-9}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{-9}\color{blue}{+9-14x }
& = & -11 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & -11 \color{blue}{+9} \\\Leftrightarrow &-23x
& = &-2\\\Leftrightarrow & \color{red}{-23}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-5}& = & 14 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-3x }
& = & 14 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & 2x \color{blue}{-3x }
& = & 14 \color{blue}{+5} \\\Leftrightarrow &-x
& = &19\\\Leftrightarrow & \color{red}{-}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{19}{-1} \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+4}\color{blue}{-4-x }
& = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -14 \color{blue}{-4} \\\Leftrightarrow &5x
& = &-18\\\Leftrightarrow & \color{red}{5}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{5} } & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)