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