Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(6x+12=14-5x\)
- \(6x+5=-5-11x\)
- \(-x-11=-2-15x\)
- \(-9x-6=14+x\)
- \(-3x-5=-12+x\)
- \(7x+2=1-2x\)
- \(3x-15=1+x\)
- \(13x-7=-9+3x\)
- \(-8x+3=15+x\)
- \(-5x-6=-11+x\)
- \(10x-13=7+3x\)
- \(6x-3=-13+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 6x \color{red}{+12}& = & 14 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12+5x }
& = & 14 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & 14 \color{blue}{-12} \\\Leftrightarrow &11x
& = &2\\\Leftrightarrow & \color{red}{11}x
& = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+5}& = & -5 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+5}\color{blue}{-5+11x }
& = & -5 \color{red}{ -11x }\color{blue}{-5+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & -5 \color{blue}{-5} \\\Leftrightarrow &17x
& = &-10\\\Leftrightarrow & \color{red}{17}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-10}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{17} } & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-11}& = & -2 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-11}\color{blue}{+11+15x }
& = & -2 \color{red}{ -15x }\color{blue}{+11+15x } \\\Leftrightarrow & -x \color{blue}{+15x }
& = & -2 \color{blue}{+11} \\\Leftrightarrow &14x
& = &9\\\Leftrightarrow & \color{red}{14}x
& = &9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-6}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-x }
& = & 14 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 14 \color{blue}{+6} \\\Leftrightarrow &-10x
& = &20\\\Leftrightarrow & \color{red}{-10}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-5}\color{blue}{+5-x }
& = & -12 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -12 \color{blue}{+5} \\\Leftrightarrow &-4x
& = &-7\\\Leftrightarrow & \color{red}{-4}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+2}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{+2}\color{blue}{-2+2x }
& = & 1 \color{red}{ -2x }\color{blue}{-2+2x } \\\Leftrightarrow & 7x \color{blue}{+2x }
& = & 1 \color{blue}{-2} \\\Leftrightarrow &9x
& = &-1\\\Leftrightarrow & \color{red}{9}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-15}\color{blue}{+15-x }
& = & 1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & 1 \color{blue}{+15} \\\Leftrightarrow &2x
& = &16\\\Leftrightarrow & \color{red}{2}x
& = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-7}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7-3x }
& = & -9 \color{red}{ +3x }\color{blue}{+7-3x } \\\Leftrightarrow & 13x \color{blue}{-3x }
& = & -9 \color{blue}{+7} \\\Leftrightarrow &10x
& = &-2\\\Leftrightarrow & \color{red}{10}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+3}\color{blue}{-3-x }
& = & 15 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 15 \color{blue}{-3} \\\Leftrightarrow &-9x
& = &12\\\Leftrightarrow & \color{red}{-9}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{12}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-6}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x }
& = & -11 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -11 \color{blue}{+6} \\\Leftrightarrow &-6x
& = &-5\\\Leftrightarrow & \color{red}{-6}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-13}& = & 7 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-3x }
& = & 7 \color{red}{ +3x }\color{blue}{+13-3x } \\\Leftrightarrow & 10x \color{blue}{-3x }
& = & 7 \color{blue}{+13} \\\Leftrightarrow &7x
& = &20\\\Leftrightarrow & \color{red}{7}x
& = &20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{20}{7} } & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-3}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3-x }
& = & -13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -13 \color{blue}{+3} \\\Leftrightarrow &5x
& = &-10\\\Leftrightarrow & \color{red}{5}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)