Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(11x+13=2-5x\)
- \(-3x+2=-14+x\)
- \(14x-2=-9+13x\)
- \(-12x+13=8+x\)
- \(6x+15=-4-5x\)
- \(-12x-7=-2+x\)
- \(9x-3=-7+4x\)
- \(-9x+15=-15+x\)
- \(-2x-12=-9+5x\)
- \(-14x-4=-5+x\)
- \(9x+13=8+4x\)
- \(7x-15=-15+10x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 11x \color{red}{+13}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13+5x }
& = & 2 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 11x \color{blue}{+5x }
& = & 2 \color{blue}{-13} \\\Leftrightarrow &16x
& = &-11\\\Leftrightarrow & \color{red}{16}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{-11}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{16} } & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2-x }
& = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -14 \color{blue}{-2} \\\Leftrightarrow &-4x
& = &-16\\\Leftrightarrow & \color{red}{-4}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-16}{-4} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-2}& = & -9 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2-13x }
& = & -9 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & 14x \color{blue}{-13x }
& = & -9 \color{blue}{+2} \\\Leftrightarrow &x
& = &-7\\\Leftrightarrow & \color{red}{}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -7 \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x }
& = & 8 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 8 \color{blue}{-13} \\\Leftrightarrow &-13x
& = &-5\\\Leftrightarrow & \color{red}{-13}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+15}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15+5x }
& = & -4 \color{red}{ -5x }\color{blue}{-15+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & -4 \color{blue}{-15} \\\Leftrightarrow &11x
& = &-19\\\Leftrightarrow & \color{red}{11}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x }
& = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -2 \color{blue}{+7} \\\Leftrightarrow &-13x
& = &5\\\Leftrightarrow & \color{red}{-13}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-3}& = & -7 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-4x }
& = & -7 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & 9x \color{blue}{-4x }
& = & -7 \color{blue}{+3} \\\Leftrightarrow &5x
& = &-4\\\Leftrightarrow & \color{red}{5}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-x }
& = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -15 \color{blue}{-15} \\\Leftrightarrow &-10x
& = &-30\\\Leftrightarrow & \color{red}{-10}x
& = &-30\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-30}{-10} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-12}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-5x }
& = & -9 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & -2x \color{blue}{-5x }
& = & -9 \color{blue}{+12} \\\Leftrightarrow &-7x
& = &3\\\Leftrightarrow & \color{red}{-7}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-4}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4-x }
& = & -5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -5 \color{blue}{+4} \\\Leftrightarrow &-15x
& = &-1\\\Leftrightarrow & \color{red}{-15}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+13}& = & 8 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13-4x }
& = & 8 \color{red}{ +4x }\color{blue}{-13-4x } \\\Leftrightarrow & 9x \color{blue}{-4x }
& = & 8 \color{blue}{-13} \\\Leftrightarrow &5x
& = &-5\\\Leftrightarrow & \color{red}{5}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-15}& = & -15 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15-10x }
& = & -15 \color{red}{ +10x }\color{blue}{+15-10x } \\\Leftrightarrow & 7x \color{blue}{-10x }
& = & -15 \color{blue}{+15} \\\Leftrightarrow &-3x
& = &0\\\Leftrightarrow & \color{red}{-3}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)