Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(7x+11=-7-9x\)
- \(-12x+4=-14+13x\)
- \(7x-2=15+3x\)
- \(-3x+5=14+13x\)
- \(14x-4=12+9x\)
- \(x-2=13+12x\)
- \(-2x+1=-9+13x\)
- \(3x-13=-6-5x\)
- \(6x+3=-12+x\)
- \(3x+11=13+11x\)
- \(2x-13=-1+x\)
- \(-12x-12=9+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 7x \color{red}{+11}& = & -7 \color{red}{ -9x } \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11+9x }
& = & -7 \color{red}{ -9x }\color{blue}{-11+9x } \\\Leftrightarrow & 7x \color{blue}{+9x }
& = & -7 \color{blue}{-11} \\\Leftrightarrow &16x
& = &-18\\\Leftrightarrow & \color{red}{16}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{-18}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+4}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x }
& = & -14 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -14 \color{blue}{-4} \\\Leftrightarrow &-25x
& = &-18\\\Leftrightarrow & \color{red}{-25}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-18}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{18}{25} } & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-2}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2-3x }
& = & 15 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & 7x \color{blue}{-3x }
& = & 15 \color{blue}{+2} \\\Leftrightarrow &4x
& = &17\\\Leftrightarrow & \color{red}{4}x
& = &17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+5}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x }
& = & 14 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x }
& = & 14 \color{blue}{-5} \\\Leftrightarrow &-16x
& = &9\\\Leftrightarrow & \color{red}{-16}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-4}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4-9x }
& = & 12 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 14x \color{blue}{-9x }
& = & 12 \color{blue}{+4} \\\Leftrightarrow &5x
& = &16\\\Leftrightarrow & \color{red}{5}x
& = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-2}& = & 13 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2-12x }
& = & 13 \color{red}{ +12x }\color{blue}{+2-12x } \\\Leftrightarrow & x \color{blue}{-12x }
& = & 13 \color{blue}{+2} \\\Leftrightarrow &-11x
& = &15\\\Leftrightarrow & \color{red}{-11}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+1}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1-13x }
& = & -9 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -2x \color{blue}{-13x }
& = & -9 \color{blue}{-1} \\\Leftrightarrow &-15x
& = &-10\\\Leftrightarrow & \color{red}{-15}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-13}& = & -6 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13+5x }
& = & -6 \color{red}{ -5x }\color{blue}{+13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x }
& = & -6 \color{blue}{+13} \\\Leftrightarrow &8x
& = &7\\\Leftrightarrow & \color{red}{8}x
& = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3-x }
& = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -12 \color{blue}{-3} \\\Leftrightarrow &5x
& = &-15\\\Leftrightarrow & \color{red}{5}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+11}& = & 13 \color{red}{ +11x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11-11x }
& = & 13 \color{red}{ +11x }\color{blue}{-11-11x } \\\Leftrightarrow & 3x \color{blue}{-11x }
& = & 13 \color{blue}{-11} \\\Leftrightarrow &-8x
& = &2\\\Leftrightarrow & \color{red}{-8}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13-x }
& = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -1 \color{blue}{+13} \\\Leftrightarrow &x
& = &12\\\Leftrightarrow & \color{red}{}x
& = &12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 12 \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-12}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x }
& = & 9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 9 \color{blue}{+12} \\\Leftrightarrow &-13x
& = &21\\\Leftrightarrow & \color{red}{-13}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)