Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-6x-11=-14+7x\)
- \(4x-14=14+5x\)
- \(13x+15=6+x\)
- \(-x-5=9+13x\)
- \(6x-15=-13+x\)
- \(-9x+8=7+x\)
- \(-14x+5=10+x\)
- \(2x+14=-14+5x\)
- \(10x+7=9+x\)
- \(9x-11=-1-8x\)
- \(-3x-10=-11+x\)
- \(11x+6=1+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -6x \color{red}{-11}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11-7x }
& = & -14 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -14 \color{blue}{+11} \\\Leftrightarrow &-13x
& = &-3\\\Leftrightarrow & \color{red}{-13}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-14}& = & 14 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-5x }
& = & 14 \color{red}{ +5x }\color{blue}{+14-5x } \\\Leftrightarrow & 4x \color{blue}{-5x }
& = & 14 \color{blue}{+14} \\\Leftrightarrow &-x
& = &28\\\Leftrightarrow & \color{red}{-}x
& = &28\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{28}{-1} \\\Leftrightarrow & \color{green}{ x = -28 } & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+15}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15-x }
& = & 6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 13x \color{blue}{-x }
& = & 6 \color{blue}{-15} \\\Leftrightarrow &12x
& = &-9\\\Leftrightarrow & \color{red}{12}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-5}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -x \color{red}{-5}\color{blue}{+5-13x }
& = & 9 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & -x \color{blue}{-13x }
& = & 9 \color{blue}{+5} \\\Leftrightarrow &-14x
& = &14\\\Leftrightarrow & \color{red}{-14}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{14}{-14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-x }
& = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -13 \color{blue}{+15} \\\Leftrightarrow &5x
& = &2\\\Leftrightarrow & \color{red}{5}x
& = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+8}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+8}\color{blue}{-8-x }
& = & 7 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 7 \color{blue}{-8} \\\Leftrightarrow &-10x
& = &-1\\\Leftrightarrow & \color{red}{-10}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+5}\color{blue}{-5-x }
& = & 10 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 10 \color{blue}{-5} \\\Leftrightarrow &-15x
& = &5\\\Leftrightarrow & \color{red}{-15}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+14}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-5x }
& = & -14 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 2x \color{blue}{-5x }
& = & -14 \color{blue}{-14} \\\Leftrightarrow &-3x
& = &-28\\\Leftrightarrow & \color{red}{-3}x
& = &-28\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-28}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{28}{3} } & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+7}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+7}\color{blue}{-7-x }
& = & 9 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & 9 \color{blue}{-7} \\\Leftrightarrow &9x
& = &2\\\Leftrightarrow & \color{red}{9}x
& = &2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-11}& = & -1 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+8x }
& = & -1 \color{red}{ -8x }\color{blue}{+11+8x } \\\Leftrightarrow & 9x \color{blue}{+8x }
& = & -1 \color{blue}{+11} \\\Leftrightarrow &17x
& = &10\\\Leftrightarrow & \color{red}{17}x
& = &10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-10}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10-x }
& = & -11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -11 \color{blue}{+10} \\\Leftrightarrow &-4x
& = &-1\\\Leftrightarrow & \color{red}{-4}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+6}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6-8x }
& = & 1 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & 11x \color{blue}{-8x }
& = & 1 \color{blue}{-6} \\\Leftrightarrow &3x
& = &-5\\\Leftrightarrow & \color{red}{3}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-5}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)