Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(5x-11=8-7x\)
- \(8x-5=3-13x\)
- \(-x+8=2+12x\)
- \(x-6=-7+12x\)
- \(-14x-10=8+x\)
- \(-6x-12=5+x\)
- \(14x-4=12-13x\)
- \(-14x-14=-14+x\)
- \(-15x+9=-5+13x\)
- \(4x-15=2-7x\)
- \(-4x+12=-7+x\)
- \(-4x-6=6+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 5x \color{red}{-11}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+7x }
& = & 8 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & 5x \color{blue}{+7x }
& = & 8 \color{blue}{+11} \\\Leftrightarrow &12x
& = &19\\\Leftrightarrow & \color{red}{12}x
& = &19\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{19}{12} \\\Leftrightarrow & \color{green}{ x = \frac{19}{12} } & & \\ & V = \left\{ \frac{19}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-5}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5+13x }
& = & 3 \color{red}{ -13x }\color{blue}{+5+13x } \\\Leftrightarrow & 8x \color{blue}{+13x }
& = & 3 \color{blue}{+5} \\\Leftrightarrow &21x
& = &8\\\Leftrightarrow & \color{red}{21}x
& = &8\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{8}{21} \\\Leftrightarrow & \color{green}{ x = \frac{8}{21} } & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+8}& = & 2 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+8}\color{blue}{-8-12x }
& = & 2 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & -x \color{blue}{-12x }
& = & 2 \color{blue}{-8} \\\Leftrightarrow &-13x
& = &-6\\\Leftrightarrow & \color{red}{-13}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-6}& = & -7 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-12x }
& = & -7 \color{red}{ +12x }\color{blue}{+6-12x } \\\Leftrightarrow & x \color{blue}{-12x }
& = & -7 \color{blue}{+6} \\\Leftrightarrow &-11x
& = &-1\\\Leftrightarrow & \color{red}{-11}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-10}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10-x }
& = & 8 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 8 \color{blue}{+10} \\\Leftrightarrow &-15x
& = &18\\\Leftrightarrow & \color{red}{-15}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-x }
& = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 5 \color{blue}{+12} \\\Leftrightarrow &-7x
& = &17\\\Leftrightarrow & \color{red}{-7}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-4}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4+13x }
& = & 12 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & 12 \color{blue}{+4} \\\Leftrightarrow &27x
& = &16\\\Leftrightarrow & \color{red}{27}x
& = &16\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{16}{27} \\\Leftrightarrow & \color{green}{ x = \frac{16}{27} } & & \\ & V = \left\{ \frac{16}{27} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-14}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x }
& = & -14 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -14 \color{blue}{+14} \\\Leftrightarrow &-15x
& = &0\\\Leftrightarrow & \color{red}{-15}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+9}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-13x }
& = & -5 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -5 \color{blue}{-9} \\\Leftrightarrow &-28x
& = &-14\\\Leftrightarrow & \color{red}{-28}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-14}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-15}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15+7x }
& = & 2 \color{red}{ -7x }\color{blue}{+15+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & 2 \color{blue}{+15} \\\Leftrightarrow &11x
& = &17\\\Leftrightarrow & \color{red}{11}x
& = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12-x }
& = & -7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -7 \color{blue}{-12} \\\Leftrightarrow &-5x
& = &-19\\\Leftrightarrow & \color{red}{-5}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-6}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6-13x }
& = & 6 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -4x \color{blue}{-13x }
& = & 6 \color{blue}{+6} \\\Leftrightarrow &-17x
& = &12\\\Leftrightarrow & \color{red}{-17}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{12}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)