Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(13x-9=7-12x\)
- \(8x+1=1-7x\)
- \(12x-3=10-11x\)
- \(-12x-14=-11+x\)
- \(-8x-12=-2+x\)
- \(-8x-13=-2+x\)
- \(11x-13=9-2x\)
- \(-3x-3=7+x\)
- \(-8x-13=8+9x\)
- \(-13x+5=15+10x\)
- \(10x-3=-11+x\)
- \(4x-14=-7-7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 13x \color{red}{-9}& = & 7 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+12x }
& = & 7 \color{red}{ -12x }\color{blue}{+9+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & 7 \color{blue}{+9} \\\Leftrightarrow &25x
& = &16\\\Leftrightarrow & \color{red}{25}x
& = &16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+1}& = & 1 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+7x }
& = & 1 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & 1 \color{blue}{-1} \\\Leftrightarrow &15x
& = &0\\\Leftrightarrow & \color{red}{15}x
& = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-3}& = & 10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3+11x }
& = & 10 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 10 \color{blue}{+3} \\\Leftrightarrow &23x
& = &13\\\Leftrightarrow & \color{red}{23}x
& = &13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{13}{23} } & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-14}\color{blue}{+14-x }
& = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -11 \color{blue}{+14} \\\Leftrightarrow &-13x
& = &3\\\Leftrightarrow & \color{red}{-13}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-12}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12-x }
& = & -2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -2 \color{blue}{+12} \\\Leftrightarrow &-9x
& = &10\\\Leftrightarrow & \color{red}{-9}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-x }
& = & -2 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -2 \color{blue}{+13} \\\Leftrightarrow &-9x
& = &11\\\Leftrightarrow & \color{red}{-9}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-13}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+2x }
& = & 9 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 11x \color{blue}{+2x }
& = & 9 \color{blue}{+13} \\\Leftrightarrow &13x
& = &22\\\Leftrightarrow & \color{red}{13}x
& = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-3}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-x }
& = & 7 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 7 \color{blue}{+3} \\\Leftrightarrow &-4x
& = &10\\\Leftrightarrow & \color{red}{-4}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{10}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-13}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-13}\color{blue}{+13-9x }
& = & 8 \color{red}{ +9x }\color{blue}{+13-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & 8 \color{blue}{+13} \\\Leftrightarrow &-17x
& = &21\\\Leftrightarrow & \color{red}{-17}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{17} } & & \\ & V = \left\{ \frac{-21}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+5}& = & 15 \color{red}{ +10x } \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5-10x }
& = & 15 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & -13x \color{blue}{-10x }
& = & 15 \color{blue}{-5} \\\Leftrightarrow &-23x
& = &10\\\Leftrightarrow & \color{red}{-23}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{10}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{23} } & & \\ & V = \left\{ \frac{-10}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-3}\color{blue}{+3-x }
& = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & -11 \color{blue}{+3} \\\Leftrightarrow &9x
& = &-8\\\Leftrightarrow & \color{red}{9}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-14}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14+7x }
& = & -7 \color{red}{ -7x }\color{blue}{+14+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & -7 \color{blue}{+14} \\\Leftrightarrow &11x
& = &7\\\Leftrightarrow & \color{red}{11}x
& = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)