Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-10x+8=-2+x\)
- \(-10x-2=4+x\)
- \(-8x-5=9+x\)
- \(13x+11=-14-3x\)
- \(14x-12=-14+13x\)
- \(2x-11=4+x\)
- \(-15x-3=-12+13x\)
- \(-2x-12=1+x\)
- \(-11x+3=-5+x\)
- \(12x+11=7-11x\)
- \(12x+3=-3-11x\)
- \(11x-14=9+4x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -10x \color{red}{+8}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+8}\color{blue}{-8-x }
& = & -2 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -2 \color{blue}{-8} \\\Leftrightarrow &-11x
& = &-10\\\Leftrightarrow & \color{red}{-11}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x }
& = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 4 \color{blue}{+2} \\\Leftrightarrow &-11x
& = &6\\\Leftrightarrow & \color{red}{-11}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x }
& = & 9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 9 \color{blue}{+5} \\\Leftrightarrow &-9x
& = &14\\\Leftrightarrow & \color{red}{-9}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+11}& = & -14 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11+3x }
& = & -14 \color{red}{ -3x }\color{blue}{-11+3x } \\\Leftrightarrow & 13x \color{blue}{+3x }
& = & -14 \color{blue}{-11} \\\Leftrightarrow &16x
& = &-25\\\Leftrightarrow & \color{red}{16}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}}
& = & \frac{-25}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{16} } & & \\ & V = \left\{ \frac{-25}{16} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-12}& = & -14 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12-13x }
& = & -14 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & 14x \color{blue}{-13x }
& = & -14 \color{blue}{+12} \\\Leftrightarrow &x
& = &-2\\\Leftrightarrow & \color{red}{}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11-x }
& = & 4 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 4 \color{blue}{+11} \\\Leftrightarrow &x
& = &15\\\Leftrightarrow & \color{red}{}x
& = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-3}& = & -12 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-13x }
& = & -12 \color{red}{ +13x }\color{blue}{+3-13x } \\\Leftrightarrow & -15x \color{blue}{-13x }
& = & -12 \color{blue}{+3} \\\Leftrightarrow &-28x
& = &-9\\\Leftrightarrow & \color{red}{-28}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}}
& = & \frac{-9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{9}{28} } & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-12}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12-x }
& = & 1 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 1 \color{blue}{+12} \\\Leftrightarrow &-3x
& = &13\\\Leftrightarrow & \color{red}{-3}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+3}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+3}\color{blue}{-3-x }
& = & -5 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -5 \color{blue}{-3} \\\Leftrightarrow &-12x
& = &-8\\\Leftrightarrow & \color{red}{-12}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+11}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x }
& = & 7 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 7 \color{blue}{-11} \\\Leftrightarrow &23x
& = &-4\\\Leftrightarrow & \color{red}{23}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+3}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3+11x }
& = & -3 \color{red}{ -11x }\color{blue}{-3+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -3 \color{blue}{-3} \\\Leftrightarrow &23x
& = &-6\\\Leftrightarrow & \color{red}{23}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{23} } & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-14}& = & 9 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-4x }
& = & 9 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 11x \color{blue}{-4x }
& = & 9 \color{blue}{+14} \\\Leftrightarrow &7x
& = &23\\\Leftrightarrow & \color{red}{7}x
& = &23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)