Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(6x+5=4+11x\)
- \(-13x-6=11+x\)
- \(-3x+3=4+7x\)
- \(7x+6=13-10x\)
- \(-3x-5=-4+7x\)
- \(14x-5=-9+x\)
- \(-9x-5=-12+10x\)
- \(8x+5=3+11x\)
- \(-12x+15=-12+5x\)
- \(12x+4=-7-11x\)
- \(-x-4=-14-13x\)
- \(-4x+13=15+5x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 6x \color{red}{+5}& = & 4 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5-11x }
& = & 4 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & 4 \color{blue}{-5} \\\Leftrightarrow &-5x
& = &-1\\\Leftrightarrow & \color{red}{-5}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-6}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x }
& = & 11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 11 \color{blue}{+6} \\\Leftrightarrow &-14x
& = &17\\\Leftrightarrow & \color{red}{-14}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{17}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{14} } & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+3}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-7x }
& = & 4 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & 4 \color{blue}{-3} \\\Leftrightarrow &-10x
& = &1\\\Leftrightarrow & \color{red}{-10}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+6}& = & 13 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+10x }
& = & 13 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & 7x \color{blue}{+10x }
& = & 13 \color{blue}{-6} \\\Leftrightarrow &17x
& = &7\\\Leftrightarrow & \color{red}{17}x
& = &7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-5}& = & -4 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-7x }
& = & -4 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & -4 \color{blue}{+5} \\\Leftrightarrow &-10x
& = &1\\\Leftrightarrow & \color{red}{-10}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-5}\color{blue}{+5-x }
& = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -9 \color{blue}{+5} \\\Leftrightarrow &13x
& = &-4\\\Leftrightarrow & \color{red}{13}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-5}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-10x }
& = & -12 \color{red}{ +10x }\color{blue}{+5-10x } \\\Leftrightarrow & -9x \color{blue}{-10x }
& = & -12 \color{blue}{+5} \\\Leftrightarrow &-19x
& = &-7\\\Leftrightarrow & \color{red}{-19}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-7}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+5}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 8x \color{red}{+5}\color{blue}{-5-11x }
& = & 3 \color{red}{ +11x }\color{blue}{-5-11x } \\\Leftrightarrow & 8x \color{blue}{-11x }
& = & 3 \color{blue}{-5} \\\Leftrightarrow &-3x
& = &-2\\\Leftrightarrow & \color{red}{-3}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+15}& = & -12 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-5x }
& = & -12 \color{red}{ +5x }\color{blue}{-15-5x } \\\Leftrightarrow & -12x \color{blue}{-5x }
& = & -12 \color{blue}{-15} \\\Leftrightarrow &-17x
& = &-27\\\Leftrightarrow & \color{red}{-17}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-27}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{27}{17} } & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+4}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4+11x }
& = & -7 \color{red}{ -11x }\color{blue}{-4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -7 \color{blue}{-4} \\\Leftrightarrow &23x
& = &-11\\\Leftrightarrow & \color{red}{23}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-11}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{23} } & & \\ & V = \left\{ \frac{-11}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-4}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4+13x }
& = & -14 \color{red}{ -13x }\color{blue}{+4+13x } \\\Leftrightarrow & -x \color{blue}{+13x }
& = & -14 \color{blue}{+4} \\\Leftrightarrow &12x
& = &-10\\\Leftrightarrow & \color{red}{12}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+13}& = & 15 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-5x }
& = & 15 \color{red}{ +5x }\color{blue}{-13-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & 15 \color{blue}{-13} \\\Leftrightarrow &-9x
& = &2\\\Leftrightarrow & \color{red}{-9}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)