Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x+8=-12+2x\)
- \(-6x-5=-15+7x\)
- \(10x-4=13+x\)
- \(-4x-10=-4+5x\)
- \(12x-3=12+11x\)
- \(15x+10=-6-2x\)
- \(5x+1=12+6x\)
- \(-5x-15=-2+x\)
- \(14x+10=-13-11x\)
- \(-8x-14=5+x\)
- \(-6x-3=11+7x\)
- \(-14x-8=-10+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{+8}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-2x }
& = & -12 \color{red}{ +2x }\color{blue}{-8-2x } \\\Leftrightarrow & 3x \color{blue}{-2x }
& = & -12 \color{blue}{-8} \\\Leftrightarrow &x
& = &-20\\\Leftrightarrow & \color{red}{}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-5}& = & -15 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-7x }
& = & -15 \color{red}{ +7x }\color{blue}{+5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -15 \color{blue}{+5} \\\Leftrightarrow &-13x
& = &-10\\\Leftrightarrow & \color{red}{-13}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-4}& = & 13 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4-x }
& = & 13 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & 13 \color{blue}{+4} \\\Leftrightarrow &9x
& = &17\\\Leftrightarrow & \color{red}{9}x
& = &17\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{17}{9} \\\Leftrightarrow & \color{green}{ x = \frac{17}{9} } & & \\ & V = \left\{ \frac{17}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-10}& = & -4 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-5x }
& = & -4 \color{red}{ +5x }\color{blue}{+10-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & -4 \color{blue}{+10} \\\Leftrightarrow &-9x
& = &6\\\Leftrightarrow & \color{red}{-9}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-3}& = & 12 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-11x }
& = & 12 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & 12x \color{blue}{-11x }
& = & 12 \color{blue}{+3} \\\Leftrightarrow &x
& = &15\\\Leftrightarrow & \color{red}{}x
& = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+10}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10+2x }
& = & -6 \color{red}{ -2x }\color{blue}{-10+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & -6 \color{blue}{-10} \\\Leftrightarrow &17x
& = &-16\\\Leftrightarrow & \color{red}{17}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{17} } & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+1}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1-6x }
& = & 12 \color{red}{ +6x }\color{blue}{-1-6x } \\\Leftrightarrow & 5x \color{blue}{-6x }
& = & 12 \color{blue}{-1} \\\Leftrightarrow &-x
& = &11\\\Leftrightarrow & \color{red}{-}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{11}{-1} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-15}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x }
& = & -2 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -2 \color{blue}{+15} \\\Leftrightarrow &-6x
& = &13\\\Leftrightarrow & \color{red}{-6}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+10}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+11x }
& = & -13 \color{red}{ -11x }\color{blue}{-10+11x } \\\Leftrightarrow & 14x \color{blue}{+11x }
& = & -13 \color{blue}{-10} \\\Leftrightarrow &25x
& = &-23\\\Leftrightarrow & \color{red}{25}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-23}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{25} } & & \\ & V = \left\{ \frac{-23}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14-x }
& = & 5 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 5 \color{blue}{+14} \\\Leftrightarrow &-9x
& = &19\\\Leftrightarrow & \color{red}{-9}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-3}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-3}\color{blue}{+3-7x }
& = & 11 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & 11 \color{blue}{+3} \\\Leftrightarrow &-13x
& = &14\\\Leftrightarrow & \color{red}{-13}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{13} } & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8-x }
& = & -10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -10 \color{blue}{+8} \\\Leftrightarrow &-15x
& = &-2\\\Leftrightarrow & \color{red}{-15}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{15} } & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)