Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(9x-13=-14+10x\)
- \(-3x+10=-8+10x\)
- \(-4x-15=-5+5x\)
- \(-12x-3=-11+x\)
- \(-12x+4=-2+x\)
- \(-4x+4=15+9x\)
- \(7x-14=8+2x\)
- \(14x-12=-14+3x\)
- \(7x+12=1+2x\)
- \(2x+7=-14+x\)
- \(9x-12=3-4x\)
- \(-11x+15=11+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 9x \color{red}{-13}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13-10x }
& = & -14 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 9x \color{blue}{-10x }
& = & -14 \color{blue}{+13} \\\Leftrightarrow &-x
& = &-1\\\Leftrightarrow & \color{red}{-}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+10}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10-10x }
& = & -8 \color{red}{ +10x }\color{blue}{-10-10x } \\\Leftrightarrow & -3x \color{blue}{-10x }
& = & -8 \color{blue}{-10} \\\Leftrightarrow &-13x
& = &-18\\\Leftrightarrow & \color{red}{-13}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-15}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15-5x }
& = & -5 \color{red}{ +5x }\color{blue}{+15-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & -5 \color{blue}{+15} \\\Leftrightarrow &-9x
& = &10\\\Leftrightarrow & \color{red}{-9}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{10}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3-x }
& = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -11 \color{blue}{+3} \\\Leftrightarrow &-13x
& = &-8\\\Leftrightarrow & \color{red}{-13}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+4}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-x }
& = & -2 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -2 \color{blue}{-4} \\\Leftrightarrow &-13x
& = &-6\\\Leftrightarrow & \color{red}{-13}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+4}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4-9x }
& = & 15 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & -4x \color{blue}{-9x }
& = & 15 \color{blue}{-4} \\\Leftrightarrow &-13x
& = &11\\\Leftrightarrow & \color{red}{-13}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-14}& = & 8 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14-2x }
& = & 8 \color{red}{ +2x }\color{blue}{+14-2x } \\\Leftrightarrow & 7x \color{blue}{-2x }
& = & 8 \color{blue}{+14} \\\Leftrightarrow &5x
& = &22\\\Leftrightarrow & \color{red}{5}x
& = &22\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{22}{5} \\\Leftrightarrow & \color{green}{ x = \frac{22}{5} } & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-12}& = & -14 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-3x }
& = & -14 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & 14x \color{blue}{-3x }
& = & -14 \color{blue}{+12} \\\Leftrightarrow &11x
& = &-2\\\Leftrightarrow & \color{red}{11}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+12}& = & 1 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12-2x }
& = & 1 \color{red}{ +2x }\color{blue}{-12-2x } \\\Leftrightarrow & 7x \color{blue}{-2x }
& = & 1 \color{blue}{-12} \\\Leftrightarrow &5x
& = &-11\\\Leftrightarrow & \color{red}{5}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7-x }
& = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -14 \color{blue}{-7} \\\Leftrightarrow &x
& = &-21\\\Leftrightarrow & \color{red}{}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -21 \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-12}& = & 3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-12}\color{blue}{+12+4x }
& = & 3 \color{red}{ -4x }\color{blue}{+12+4x } \\\Leftrightarrow & 9x \color{blue}{+4x }
& = & 3 \color{blue}{+12} \\\Leftrightarrow &13x
& = &15\\\Leftrightarrow & \color{red}{13}x
& = &15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+15}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15-x }
& = & 11 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 11 \color{blue}{-15} \\\Leftrightarrow &-12x
& = &-4\\\Leftrightarrow & \color{red}{-12}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)