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