Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-3x+11=12+7x\)
- \(9x+1=-6-4x\)
- \(7x-4=-7+9x\)
- \(x-11=-5+4x\)
- \(6x-15=-9+x\)
- \(5x+6=12-2x\)
- \(10x-7=-2-9x\)
- \(13x-4=-8+10x\)
- \(x+1=-15+13x\)
- \(-2x-11=13+x\)
- \(12x-4=-8+x\)
- \(13x-11=-14+14x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -3x \color{red}{+11}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+11}\color{blue}{-11-7x }
& = & 12 \color{red}{ +7x }\color{blue}{-11-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & 12 \color{blue}{-11} \\\Leftrightarrow &-10x
& = &1\\\Leftrightarrow & \color{red}{-10}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+1}& = & -6 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1+4x }
& = & -6 \color{red}{ -4x }\color{blue}{-1+4x } \\\Leftrightarrow & 9x \color{blue}{+4x }
& = & -6 \color{blue}{-1} \\\Leftrightarrow &13x
& = &-7\\\Leftrightarrow & \color{red}{13}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-4}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4-9x }
& = & -7 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 7x \color{blue}{-9x }
& = & -7 \color{blue}{+4} \\\Leftrightarrow &-2x
& = &-3\\\Leftrightarrow & \color{red}{-2}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{-3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-11}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11-4x }
& = & -5 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & x \color{blue}{-4x }
& = & -5 \color{blue}{+11} \\\Leftrightarrow &-3x
& = &6\\\Leftrightarrow & \color{red}{-3}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{6}{-3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-x }
& = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -9 \color{blue}{+15} \\\Leftrightarrow &5x
& = &6\\\Leftrightarrow & \color{red}{5}x
& = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+6}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{+6}\color{blue}{-6+2x }
& = & 12 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 5x \color{blue}{+2x }
& = & 12 \color{blue}{-6} \\\Leftrightarrow &7x
& = &6\\\Leftrightarrow & \color{red}{7}x
& = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-7}& = & -2 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+9x }
& = & -2 \color{red}{ -9x }\color{blue}{+7+9x } \\\Leftrightarrow & 10x \color{blue}{+9x }
& = & -2 \color{blue}{+7} \\\Leftrightarrow &19x
& = &5\\\Leftrightarrow & \color{red}{19}x
& = &5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-4}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4-10x }
& = & -8 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & 13x \color{blue}{-10x }
& = & -8 \color{blue}{+4} \\\Leftrightarrow &3x
& = &-4\\\Leftrightarrow & \color{red}{3}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+1}& = & -15 \color{red}{ +13x } \\\Leftrightarrow & x \color{red}{+1}\color{blue}{-1-13x }
& = & -15 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & x \color{blue}{-13x }
& = & -15 \color{blue}{-1} \\\Leftrightarrow &-12x
& = &-16\\\Leftrightarrow & \color{red}{-12}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11-x }
& = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 13 \color{blue}{+11} \\\Leftrightarrow &-3x
& = &24\\\Leftrightarrow & \color{red}{-3}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{24}{-3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-4}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4-x }
& = & -8 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -8 \color{blue}{+4} \\\Leftrightarrow &11x
& = &-4\\\Leftrightarrow & \color{red}{11}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-11}& = & -14 \color{red}{ +14x } \\\Leftrightarrow & 13x \color{red}{-11}\color{blue}{+11-14x }
& = & -14 \color{red}{ +14x }\color{blue}{+11-14x } \\\Leftrightarrow & 13x \color{blue}{-14x }
& = & -14 \color{blue}{+11} \\\Leftrightarrow &-x
& = &-3\\\Leftrightarrow & \color{red}{-}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-3}{-1} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)