Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-7x+3=10+8x\)
- \(13x+8=-11-3x\)
- \(6x-5=13+x\)
- \(7x-11=-8+12x\)
- \(-3x+7=5+10x\)
- \(5x+5=-12-7x\)
- \(x+7=-11-5x\)
- \(6x-3=3-11x\)
- \(15x-10=-7+14x\)
- \(9x-11=-6-8x\)
- \(-14x-2=-10+x\)
- \(-8x-5=8+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -7x \color{red}{+3}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-8x }
& = & 10 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x }
& = & 10 \color{blue}{-3} \\\Leftrightarrow &-15x
& = &7\\\Leftrightarrow & \color{red}{-15}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+8}& = & -11 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{+8}\color{blue}{-8+3x }
& = & -11 \color{red}{ -3x }\color{blue}{-8+3x } \\\Leftrightarrow & 13x \color{blue}{+3x }
& = & -11 \color{blue}{-8} \\\Leftrightarrow &16x
& = &-19\\\Leftrightarrow & \color{red}{16}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{-19}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{16} } & & \\ & V = \left\{ \frac{-19}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-5}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5-x }
& = & 13 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 13 \color{blue}{+5} \\\Leftrightarrow &5x
& = &18\\\Leftrightarrow & \color{red}{5}x
& = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-11}& = & -8 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-12x }
& = & -8 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 7x \color{blue}{-12x }
& = & -8 \color{blue}{+11} \\\Leftrightarrow &-5x
& = &3\\\Leftrightarrow & \color{red}{-5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+7}& = & 5 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-10x }
& = & 5 \color{red}{ +10x }\color{blue}{-7-10x } \\\Leftrightarrow & -3x \color{blue}{-10x }
& = & 5 \color{blue}{-7} \\\Leftrightarrow &-13x
& = &-2\\\Leftrightarrow & \color{red}{-13}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+5}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+5}\color{blue}{-5+7x }
& = & -12 \color{red}{ -7x }\color{blue}{-5+7x } \\\Leftrightarrow & 5x \color{blue}{+7x }
& = & -12 \color{blue}{-5} \\\Leftrightarrow &12x
& = &-17\\\Leftrightarrow & \color{red}{12}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-17}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+7}& = & -11 \color{red}{ -5x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+5x }
& = & -11 \color{red}{ -5x }\color{blue}{-7+5x } \\\Leftrightarrow & x \color{blue}{+5x }
& = & -11 \color{blue}{-7} \\\Leftrightarrow &6x
& = &-18\\\Leftrightarrow & \color{red}{6}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{-18}{6} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-3}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3+11x }
& = & 3 \color{red}{ -11x }\color{blue}{+3+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 3 \color{blue}{+3} \\\Leftrightarrow &17x
& = &6\\\Leftrightarrow & \color{red}{17}x
& = &6\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{6}{17} \\\Leftrightarrow & \color{green}{ x = \frac{6}{17} } & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-10}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10-14x }
& = & -7 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & 15x \color{blue}{-14x }
& = & -7 \color{blue}{+10} \\\Leftrightarrow &x
& = &3\\\Leftrightarrow & \color{red}{}x
& = &3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 3 \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-11}& = & -6 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-11}\color{blue}{+11+8x }
& = & -6 \color{red}{ -8x }\color{blue}{+11+8x } \\\Leftrightarrow & 9x \color{blue}{+8x }
& = & -6 \color{blue}{+11} \\\Leftrightarrow &17x
& = &5\\\Leftrightarrow & \color{red}{17}x
& = &5\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{5}{17} \\\Leftrightarrow & \color{green}{ x = \frac{5}{17} } & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2-x }
& = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -10 \color{blue}{+2} \\\Leftrightarrow &-15x
& = &-8\\\Leftrightarrow & \color{red}{-15}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x }
& = & 8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 8 \color{blue}{+5} \\\Leftrightarrow &-9x
& = &13\\\Leftrightarrow & \color{red}{-9}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{9} } & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)