Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(13x+11=8+8x\)
- \(-14x+5=1+x\)
- \(3x-3=13+4x\)
- \(12x+5=-13+x\)
- \(3x+7=-15-5x\)
- \(-7x+11=-13+x\)
- \(5x-14=8+13x\)
- \(-4x+11=14+13x\)
- \(9x-5=12-11x\)
- \(-15x-12=-10+8x\)
- \(-4x-7=-7+x\)
- \(6x-5=11-11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 13x \color{red}{+11}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11-8x }
& = & 8 \color{red}{ +8x }\color{blue}{-11-8x } \\\Leftrightarrow & 13x \color{blue}{-8x }
& = & 8 \color{blue}{-11} \\\Leftrightarrow &5x
& = &-3\\\Leftrightarrow & \color{red}{5}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+5}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x }
& = & 1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 1 \color{blue}{-5} \\\Leftrightarrow &-15x
& = &-4\\\Leftrightarrow & \color{red}{-15}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-3}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3-4x }
& = & 13 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 3x \color{blue}{-4x }
& = & 13 \color{blue}{+3} \\\Leftrightarrow &-x
& = &16\\\Leftrightarrow & \color{red}{-}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+5}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+5}\color{blue}{-5-x }
& = & -13 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -13 \color{blue}{-5} \\\Leftrightarrow &11x
& = &-18\\\Leftrightarrow & \color{red}{11}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+7}& = & -15 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7+5x }
& = & -15 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & 3x \color{blue}{+5x }
& = & -15 \color{blue}{-7} \\\Leftrightarrow &8x
& = &-22\\\Leftrightarrow & \color{red}{8}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-22}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x }
& = & -13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -13 \color{blue}{-11} \\\Leftrightarrow &-8x
& = &-24\\\Leftrightarrow & \color{red}{-8}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-24}{-8} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-14}& = & 8 \color{red}{ +13x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14-13x }
& = & 8 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 5x \color{blue}{-13x }
& = & 8 \color{blue}{+14} \\\Leftrightarrow &-8x
& = &22\\\Leftrightarrow & \color{red}{-8}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+11}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11-13x }
& = & 14 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -4x \color{blue}{-13x }
& = & 14 \color{blue}{-11} \\\Leftrightarrow &-17x
& = &3\\\Leftrightarrow & \color{red}{-17}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{3}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{17} } & & \\ & V = \left\{ \frac{-3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-5}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-5}\color{blue}{+5+11x }
& = & 12 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & 12 \color{blue}{+5} \\\Leftrightarrow &20x
& = &17\\\Leftrightarrow & \color{red}{20}x
& = &17\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{17}{20} \\\Leftrightarrow & \color{green}{ x = \frac{17}{20} } & & \\ & V = \left\{ \frac{17}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-12}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-8x }
& = & -10 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -15x \color{blue}{-8x }
& = & -10 \color{blue}{+12} \\\Leftrightarrow &-23x
& = &2\\\Leftrightarrow & \color{red}{-23}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{2}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{23} } & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-x }
& = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -7 \color{blue}{+7} \\\Leftrightarrow &-5x
& = &0\\\Leftrightarrow & \color{red}{-5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-5}& = & 11 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5+11x }
& = & 11 \color{red}{ -11x }\color{blue}{+5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 11 \color{blue}{+5} \\\Leftrightarrow &17x
& = &16\\\Leftrightarrow & \color{red}{17}x
& = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)