Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-6x+5=-13+7x\)
- \(-12x-10=9+13x\)
- \(12x-14=15+7x\)
- \(-11x+10=13+4x\)
- \(11x+13=-14+10x\)
- \(-10x+7=-14+x\)
- \(-8x+14=14+x\)
- \(-8x-10=13+x\)
- \(9x+11=-4+10x\)
- \(6x+10=2-5x\)
- \(-7x+3=8+x\)
- \(-x-12=3+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -6x \color{red}{+5}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-7x }
& = & -13 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -13 \color{blue}{-5} \\\Leftrightarrow &-13x
& = &-18\\\Leftrightarrow & \color{red}{-13}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-18}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{18}{13} } & & \\ & V = \left\{ \frac{18}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-10}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-13x }
& = & 9 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 9 \color{blue}{+10} \\\Leftrightarrow &-25x
& = &19\\\Leftrightarrow & \color{red}{-25}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{25} } & & \\ & V = \left\{ \frac{-19}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-14}& = & 15 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-7x }
& = & 15 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 12x \color{blue}{-7x }
& = & 15 \color{blue}{+14} \\\Leftrightarrow &5x
& = &29\\\Leftrightarrow & \color{red}{5}x
& = &29\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{29}{5} \\\Leftrightarrow & \color{green}{ x = \frac{29}{5} } & & \\ & V = \left\{ \frac{29}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+10}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-4x }
& = & 13 \color{red}{ +4x }\color{blue}{-10-4x } \\\Leftrightarrow & -11x \color{blue}{-4x }
& = & 13 \color{blue}{-10} \\\Leftrightarrow &-15x
& = &3\\\Leftrightarrow & \color{red}{-15}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+13}& = & -14 \color{red}{ +10x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-10x }
& = & -14 \color{red}{ +10x }\color{blue}{-13-10x } \\\Leftrightarrow & 11x \color{blue}{-10x }
& = & -14 \color{blue}{-13} \\\Leftrightarrow &x
& = &-27\\\Leftrightarrow & \color{red}{}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -27 \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+7}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x }
& = & -14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -14 \color{blue}{-7} \\\Leftrightarrow &-11x
& = &-21\\\Leftrightarrow & \color{red}{-11}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+14}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14-x }
& = & 14 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 14 \color{blue}{-14} \\\Leftrightarrow &-9x
& = &0\\\Leftrightarrow & \color{red}{-9}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x }
& = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 13 \color{blue}{+10} \\\Leftrightarrow &-9x
& = &23\\\Leftrightarrow & \color{red}{-9}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+11}& = & -4 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+11}\color{blue}{-11-10x }
& = & -4 \color{red}{ +10x }\color{blue}{-11-10x } \\\Leftrightarrow & 9x \color{blue}{-10x }
& = & -4 \color{blue}{-11} \\\Leftrightarrow &-x
& = &-15\\\Leftrightarrow & \color{red}{-}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-15}{-1} \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+10}& = & 2 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10+5x }
& = & 2 \color{red}{ -5x }\color{blue}{-10+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & 2 \color{blue}{-10} \\\Leftrightarrow &11x
& = &-8\\\Leftrightarrow & \color{red}{11}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-8}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+3}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-x }
& = & 8 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & 8 \color{blue}{-3} \\\Leftrightarrow &-8x
& = &5\\\Leftrightarrow & \color{red}{-8}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{5}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-12}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & -x \color{red}{-12}\color{blue}{+12-8x }
& = & 3 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & -x \color{blue}{-8x }
& = & 3 \color{blue}{+12} \\\Leftrightarrow &-9x
& = &15\\\Leftrightarrow & \color{red}{-9}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)