Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(11x-8=14-8x\)
- \(3x-7=13-2x\)
- \(-3x+13=-6+x\)
- \(14x-14=2-11x\)
- \(-2x-14=-1+x\)
- \(x-6=13+15x\)
- \(2x-10=-6+3x\)
- \(13x-9=10-6x\)
- \(-5x+13=-10+x\)
- \(-3x-6=-7+x\)
- \(4x-3=-3-7x\)
- \(8x-13=2-7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 11x \color{red}{-8}& = & 14 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+8x }
& = & 14 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & 11x \color{blue}{+8x }
& = & 14 \color{blue}{+8} \\\Leftrightarrow &19x
& = &22\\\Leftrightarrow & \color{red}{19}x
& = &22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{22}{19} } & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-7}& = & 13 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7+2x }
& = & 13 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & 13 \color{blue}{+7} \\\Leftrightarrow &5x
& = &20\\\Leftrightarrow & \color{red}{5}x
& = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13-x }
& = & -6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -6 \color{blue}{-13} \\\Leftrightarrow &-4x
& = &-19\\\Leftrightarrow & \color{red}{-4}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-14}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14+11x }
& = & 2 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 14x \color{blue}{+11x }
& = & 2 \color{blue}{+14} \\\Leftrightarrow &25x
& = &16\\\Leftrightarrow & \color{red}{25}x
& = &16\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{16}{25} \\\Leftrightarrow & \color{green}{ x = \frac{16}{25} } & & \\ & V = \left\{ \frac{16}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-14}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14-x }
& = & -1 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & -1 \color{blue}{+14} \\\Leftrightarrow &-3x
& = &13\\\Leftrightarrow & \color{red}{-3}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-6}& = & 13 \color{red}{ +15x } \\\Leftrightarrow & x \color{red}{-6}\color{blue}{+6-15x }
& = & 13 \color{red}{ +15x }\color{blue}{+6-15x } \\\Leftrightarrow & x \color{blue}{-15x }
& = & 13 \color{blue}{+6} \\\Leftrightarrow &-14x
& = &19\\\Leftrightarrow & \color{red}{-14}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-10}& = & -6 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-3x }
& = & -6 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 2x \color{blue}{-3x }
& = & -6 \color{blue}{+10} \\\Leftrightarrow &-x
& = &4\\\Leftrightarrow & \color{red}{-}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-9}& = & 10 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-9}\color{blue}{+9+6x }
& = & 10 \color{red}{ -6x }\color{blue}{+9+6x } \\\Leftrightarrow & 13x \color{blue}{+6x }
& = & 10 \color{blue}{+9} \\\Leftrightarrow &19x
& = &19\\\Leftrightarrow & \color{red}{19}x
& = &19\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{19}{19} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+13}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x }
& = & -10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -10 \color{blue}{-13} \\\Leftrightarrow &-6x
& = &-23\\\Leftrightarrow & \color{red}{-6}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-6}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x }
& = & -7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & -7 \color{blue}{+6} \\\Leftrightarrow &-4x
& = &-1\\\Leftrightarrow & \color{red}{-4}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-3}& = & -3 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3+7x }
& = & -3 \color{red}{ -7x }\color{blue}{+3+7x } \\\Leftrightarrow & 4x \color{blue}{+7x }
& = & -3 \color{blue}{+3} \\\Leftrightarrow &11x
& = &0\\\Leftrightarrow & \color{red}{11}x
& = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-13}& = & 2 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13+7x }
& = & 2 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 8x \color{blue}{+7x }
& = & 2 \color{blue}{+13} \\\Leftrightarrow &15x
& = &15\\\Leftrightarrow & \color{red}{15}x
& = &15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}}
& = & \frac{15}{15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)