Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-13x+4=-14+7x\)
- \(6x-8=-8+x\)
- \(7x+5=3-10x\)
- \(5x-8=-4-12x\)
- \(-x+13=4-8x\)
- \(-14x+9=-3+x\)
- \(14x-3=-9+x\)
- \(3x-3=-2+7x\)
- \(2x+15=-3+7x\)
- \(-3x-6=-8+4x\)
- \(-12x-8=4+x\)
- \(-9x-10=-15+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -13x \color{red}{+4}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-7x }
& = & -14 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -14 \color{blue}{-4} \\\Leftrightarrow &-20x
& = &-18\\\Leftrightarrow & \color{red}{-20}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{-18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-8}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-8}\color{blue}{+8-x }
& = & -8 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -8 \color{blue}{+8} \\\Leftrightarrow &5x
& = &0\\\Leftrightarrow & \color{red}{5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+5}& = & 3 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+5}\color{blue}{-5+10x }
& = & 3 \color{red}{ -10x }\color{blue}{-5+10x } \\\Leftrightarrow & 7x \color{blue}{+10x }
& = & 3 \color{blue}{-5} \\\Leftrightarrow &17x
& = &-2\\\Leftrightarrow & \color{red}{17}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-8}& = & -4 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8+12x }
& = & -4 \color{red}{ -12x }\color{blue}{+8+12x } \\\Leftrightarrow & 5x \color{blue}{+12x }
& = & -4 \color{blue}{+8} \\\Leftrightarrow &17x
& = &4\\\Leftrightarrow & \color{red}{17}x
& = &4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{4}{17} } & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+13}& = & 4 \color{red}{ -8x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13+8x }
& = & 4 \color{red}{ -8x }\color{blue}{-13+8x } \\\Leftrightarrow & -x \color{blue}{+8x }
& = & 4 \color{blue}{-13} \\\Leftrightarrow &7x
& = &-9\\\Leftrightarrow & \color{red}{7}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x }
& = & -3 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -3 \color{blue}{-9} \\\Leftrightarrow &-15x
& = &-12\\\Leftrightarrow & \color{red}{-15}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-3}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3-x }
& = & -9 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -9 \color{blue}{+3} \\\Leftrightarrow &13x
& = &-6\\\Leftrightarrow & \color{red}{13}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-3}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{-3}\color{blue}{+3-7x }
& = & -2 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 3x \color{blue}{-7x }
& = & -2 \color{blue}{+3} \\\Leftrightarrow &-4x
& = &1\\\Leftrightarrow & \color{red}{-4}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+15}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-7x }
& = & -3 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & 2x \color{blue}{-7x }
& = & -3 \color{blue}{-15} \\\Leftrightarrow &-5x
& = &-18\\\Leftrightarrow & \color{red}{-5}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-18}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-6}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-4x }
& = & -8 \color{red}{ +4x }\color{blue}{+6-4x } \\\Leftrightarrow & -3x \color{blue}{-4x }
& = & -8 \color{blue}{+6} \\\Leftrightarrow &-7x
& = &-2\\\Leftrightarrow & \color{red}{-7}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-8}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8-x }
& = & 4 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 4 \color{blue}{+8} \\\Leftrightarrow &-13x
& = &12\\\Leftrightarrow & \color{red}{-13}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10-x }
& = & -15 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -15 \color{blue}{+10} \\\Leftrightarrow &-10x
& = &-5\\\Leftrightarrow & \color{red}{-10}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)