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