Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(14x-13=11+x\)
- \(-7x-11=10+4x\)
- \(7x+3=4+3x\)
- \(3x+9=-13+7x\)
- \(-6x+3=-10+x\)
- \(3x-8=14+13x\)
- \(3x+13=15-5x\)
- \(14x-8=8+5x\)
- \(6x+7=-15+11x\)
- \(13x+14=-4-12x\)
- \(-9x+2=-3+x\)
- \(-x-13=7-8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 14x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13-x }
& = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & 11 \color{blue}{+13} \\\Leftrightarrow &13x
& = &24\\\Leftrightarrow & \color{red}{13}x
& = &24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{24}{13} } & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-11}& = & 10 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-4x }
& = & 10 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & -7x \color{blue}{-4x }
& = & 10 \color{blue}{+11} \\\Leftrightarrow &-11x
& = &21\\\Leftrightarrow & \color{red}{-11}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+3}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3-3x }
& = & 4 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 7x \color{blue}{-3x }
& = & 4 \color{blue}{-3} \\\Leftrightarrow &4x
& = &1\\\Leftrightarrow & \color{red}{4}x
& = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+9}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9-7x }
& = & -13 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 3x \color{blue}{-7x }
& = & -13 \color{blue}{-9} \\\Leftrightarrow &-4x
& = &-22\\\Leftrightarrow & \color{red}{-4}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+3}\color{blue}{-3-x }
& = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -10 \color{blue}{-3} \\\Leftrightarrow &-7x
& = &-13\\\Leftrightarrow & \color{red}{-7}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-8}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8-13x }
& = & 14 \color{red}{ +13x }\color{blue}{+8-13x } \\\Leftrightarrow & 3x \color{blue}{-13x }
& = & 14 \color{blue}{+8} \\\Leftrightarrow &-10x
& = &22\\\Leftrightarrow & \color{red}{-10}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{22}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+13}& = & 15 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13+5x }
& = & 15 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 3x \color{blue}{+5x }
& = & 15 \color{blue}{-13} \\\Leftrightarrow &8x
& = &2\\\Leftrightarrow & \color{red}{8}x
& = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-8}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8-5x }
& = & 8 \color{red}{ +5x }\color{blue}{+8-5x } \\\Leftrightarrow & 14x \color{blue}{-5x }
& = & 8 \color{blue}{+8} \\\Leftrightarrow &9x
& = &16\\\Leftrightarrow & \color{red}{9}x
& = &16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+7}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-11x }
& = & -15 \color{red}{ +11x }\color{blue}{-7-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & -15 \color{blue}{-7} \\\Leftrightarrow &-5x
& = &-22\\\Leftrightarrow & \color{red}{-5}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-22}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+14}& = & -4 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14+12x }
& = & -4 \color{red}{ -12x }\color{blue}{-14+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & -4 \color{blue}{-14} \\\Leftrightarrow &25x
& = &-18\\\Leftrightarrow & \color{red}{25}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-18}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{25} } & & \\ & V = \left\{ \frac{-18}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+2}\color{blue}{-2-x }
& = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -3 \color{blue}{-2} \\\Leftrightarrow &-10x
& = &-5\\\Leftrightarrow & \color{red}{-10}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-13}& = & 7 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+8x }
& = & 7 \color{red}{ -8x }\color{blue}{+13+8x } \\\Leftrightarrow & -x \color{blue}{+8x }
& = & 7 \color{blue}{+13} \\\Leftrightarrow &7x
& = &20\\\Leftrightarrow & \color{red}{7}x
& = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)