Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(14x+12=14-13x\)
- \(x-8=-10+14x\)
- \(-11x-7=-6+12x\)
- \(-3x-1=13+x\)
- \(11x-14=7+4x\)
- \(-8x-3=-14+x\)
- \(-14x-13=7+x\)
- \(-7x-7=-7+x\)
- \(11x-10=12-2x\)
- \(4x-5=13+5x\)
- \(6x-13=11+x\)
- \(-6x-6=11+7x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 14x \color{red}{+12}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+12}\color{blue}{-12+13x }
& = & 14 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & 14 \color{blue}{-12} \\\Leftrightarrow &27x
& = &2\\\Leftrightarrow & \color{red}{27}x
& = &2\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{2}{27} \\\Leftrightarrow & \color{green}{ x = \frac{2}{27} } & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-8}& = & -10 \color{red}{ +14x } \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8-14x }
& = & -10 \color{red}{ +14x }\color{blue}{+8-14x } \\\Leftrightarrow & x \color{blue}{-14x }
& = & -10 \color{blue}{+8} \\\Leftrightarrow &-13x
& = &-2\\\Leftrightarrow & \color{red}{-13}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-7}& = & -6 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-7}\color{blue}{+7-12x }
& = & -6 \color{red}{ +12x }\color{blue}{+7-12x } \\\Leftrightarrow & -11x \color{blue}{-12x }
& = & -6 \color{blue}{+7} \\\Leftrightarrow &-23x
& = &1\\\Leftrightarrow & \color{red}{-23}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-1}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-1}\color{blue}{+1-x }
& = & 13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 13 \color{blue}{+1} \\\Leftrightarrow &-4x
& = &14\\\Leftrightarrow & \color{red}{-4}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-14}& = & 7 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-4x }
& = & 7 \color{red}{ +4x }\color{blue}{+14-4x } \\\Leftrightarrow & 11x \color{blue}{-4x }
& = & 7 \color{blue}{+14} \\\Leftrightarrow &7x
& = &21\\\Leftrightarrow & \color{red}{7}x
& = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-3}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3-x }
& = & -14 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -14 \color{blue}{+3} \\\Leftrightarrow &-9x
& = &-11\\\Leftrightarrow & \color{red}{-9}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13-x }
& = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 7 \color{blue}{+13} \\\Leftrightarrow &-15x
& = &20\\\Leftrightarrow & \color{red}{-15}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7-x }
& = & -7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -7 \color{blue}{+7} \\\Leftrightarrow &-8x
& = &0\\\Leftrightarrow & \color{red}{-8}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-10}& = & 12 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10+2x }
& = & 12 \color{red}{ -2x }\color{blue}{+10+2x } \\\Leftrightarrow & 11x \color{blue}{+2x }
& = & 12 \color{blue}{+10} \\\Leftrightarrow &13x
& = &22\\\Leftrightarrow & \color{red}{13}x
& = &22\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{22}{13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-5}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5-5x }
& = & 13 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & 4x \color{blue}{-5x }
& = & 13 \color{blue}{+5} \\\Leftrightarrow &-x
& = &18\\\Leftrightarrow & \color{red}{-}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{18}{-1} \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-13}& = & 11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13-x }
& = & 11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 11 \color{blue}{+13} \\\Leftrightarrow &5x
& = &24\\\Leftrightarrow & \color{red}{5}x
& = &24\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{24}{5} \\\Leftrightarrow & \color{green}{ x = \frac{24}{5} } & & \\ & V = \left\{ \frac{24}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-6}& = & 11 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6-7x }
& = & 11 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & 11 \color{blue}{+6} \\\Leftrightarrow &-13x
& = &17\\\Leftrightarrow & \color{red}{-13}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{17}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{13} } & & \\ & V = \left\{ \frac{-17}{13} \right\} & \\\end{align}\)