Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x+5=-5+4x\)
- \(5x+3=2-4x\)
- \(-11x+8=-3+3x\)
- \(2x+4=-1+3x\)
- \(13x-6=8-4x\)
- \(-11x+10=-12+x\)
- \(-13x-3=-11+7x\)
- \(5x+12=-14+11x\)
- \(6x+3=-3-5x\)
- \(5x+11=15+x\)
- \(12x+1=-12-11x\)
- \(9x-14=-7+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{+5}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5-4x }
& = & -5 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & 3x \color{blue}{-4x }
& = & -5 \color{blue}{-5} \\\Leftrightarrow &-x
& = &-10\\\Leftrightarrow & \color{red}{-}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-10}{-1} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+3}& = & 2 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3+4x }
& = & 2 \color{red}{ -4x }\color{blue}{-3+4x } \\\Leftrightarrow & 5x \color{blue}{+4x }
& = & 2 \color{blue}{-3} \\\Leftrightarrow &9x
& = &-1\\\Leftrightarrow & \color{red}{9}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+8}& = & -3 \color{red}{ +3x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-3x }
& = & -3 \color{red}{ +3x }\color{blue}{-8-3x } \\\Leftrightarrow & -11x \color{blue}{-3x }
& = & -3 \color{blue}{-8} \\\Leftrightarrow &-14x
& = &-11\\\Leftrightarrow & \color{red}{-14}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+4}& = & -1 \color{red}{ +3x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-3x }
& = & -1 \color{red}{ +3x }\color{blue}{-4-3x } \\\Leftrightarrow & 2x \color{blue}{-3x }
& = & -1 \color{blue}{-4} \\\Leftrightarrow &-x
& = &-5\\\Leftrightarrow & \color{red}{-}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-5}{-1} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-6}& = & 8 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6+4x }
& = & 8 \color{red}{ -4x }\color{blue}{+6+4x } \\\Leftrightarrow & 13x \color{blue}{+4x }
& = & 8 \color{blue}{+6} \\\Leftrightarrow &17x
& = &14\\\Leftrightarrow & \color{red}{17}x
& = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+10}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10-x }
& = & -12 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -12 \color{blue}{-10} \\\Leftrightarrow &-12x
& = &-22\\\Leftrightarrow & \color{red}{-12}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-22}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-3}& = & -11 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3-7x }
& = & -11 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & -13x \color{blue}{-7x }
& = & -11 \color{blue}{+3} \\\Leftrightarrow &-20x
& = &-8\\\Leftrightarrow & \color{red}{-20}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{-8}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+12}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12-11x }
& = & -14 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 5x \color{blue}{-11x }
& = & -14 \color{blue}{-12} \\\Leftrightarrow &-6x
& = &-26\\\Leftrightarrow & \color{red}{-6}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{3} } & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+3}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3+5x }
& = & -3 \color{red}{ -5x }\color{blue}{-3+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & -3 \color{blue}{-3} \\\Leftrightarrow &11x
& = &-6\\\Leftrightarrow & \color{red}{11}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+11}\color{blue}{-11-x }
& = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 5x \color{blue}{-x }
& = & 15 \color{blue}{-11} \\\Leftrightarrow &4x
& = &4\\\Leftrightarrow & \color{red}{4}x
& = &4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{4}{4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+1}& = & -12 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1+11x }
& = & -12 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -12 \color{blue}{-1} \\\Leftrightarrow &23x
& = &-13\\\Leftrightarrow & \color{red}{23}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-13}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{23} } & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-14}& = & -7 \color{red}{ +8x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14-8x }
& = & -7 \color{red}{ +8x }\color{blue}{+14-8x } \\\Leftrightarrow & 9x \color{blue}{-8x }
& = & -7 \color{blue}{+14} \\\Leftrightarrow &x
& = &7\\\Leftrightarrow & \color{red}{}x
& = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)