Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-12x+10=3+13x\)
- \(-3x+5=-3+13x\)
- \(8x+4=-11+x\)
- \(-11x-6=12+9x\)
- \(12x+8=-11-11x\)
- \(-11x-15=-9+x\)
- \(3x+10=1-8x\)
- \(x-9=-2-7x\)
- \(-5x-1=-13+8x\)
- \(12x-14=6+7x\)
- \(9x+6=-9-11x\)
- \(-8x+2=-3+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -12x \color{red}{+10}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-13x }
& = & 3 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 3 \color{blue}{-10} \\\Leftrightarrow &-25x
& = &-7\\\Leftrightarrow & \color{red}{-25}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-7}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{7}{25} } & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+5}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-13x }
& = & -3 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -3x \color{blue}{-13x }
& = & -3 \color{blue}{-5} \\\Leftrightarrow &-16x
& = &-8\\\Leftrightarrow & \color{red}{-16}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-8}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4-x }
& = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & -11 \color{blue}{-4} \\\Leftrightarrow &7x
& = &-15\\\Leftrightarrow & \color{red}{7}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{7} } & & \\ & V = \left\{ \frac{-15}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-6}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-9x }
& = & 12 \color{red}{ +9x }\color{blue}{+6-9x } \\\Leftrightarrow & -11x \color{blue}{-9x }
& = & 12 \color{blue}{+6} \\\Leftrightarrow &-20x
& = &18\\\Leftrightarrow & \color{red}{-20}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}}
& = & \frac{18}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+8}& = & -11 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+8}\color{blue}{-8+11x }
& = & -11 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & -11 \color{blue}{-8} \\\Leftrightarrow &23x
& = &-19\\\Leftrightarrow & \color{red}{23}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-15}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x }
& = & -9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -9 \color{blue}{+15} \\\Leftrightarrow &-12x
& = &6\\\Leftrightarrow & \color{red}{-12}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+10}& = & 1 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10+8x }
& = & 1 \color{red}{ -8x }\color{blue}{-10+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & 1 \color{blue}{-10} \\\Leftrightarrow &11x
& = &-9\\\Leftrightarrow & \color{red}{11}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-9}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+7x }
& = & -2 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & x \color{blue}{+7x }
& = & -2 \color{blue}{+9} \\\Leftrightarrow &8x
& = &7\\\Leftrightarrow & \color{red}{8}x
& = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-1}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1-8x }
& = & -13 \color{red}{ +8x }\color{blue}{+1-8x } \\\Leftrightarrow & -5x \color{blue}{-8x }
& = & -13 \color{blue}{+1} \\\Leftrightarrow &-13x
& = &-12\\\Leftrightarrow & \color{red}{-13}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-14}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-14}\color{blue}{+14-7x }
& = & 6 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 12x \color{blue}{-7x }
& = & 6 \color{blue}{+14} \\\Leftrightarrow &5x
& = &20\\\Leftrightarrow & \color{red}{5}x
& = &20\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{20}{5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+6}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+11x }
& = & -9 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & -9 \color{blue}{-6} \\\Leftrightarrow &20x
& = &-15\\\Leftrightarrow & \color{red}{20}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-15}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+2}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{+2}\color{blue}{-2-11x }
& = & -3 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & -8x \color{blue}{-11x }
& = & -3 \color{blue}{-2} \\\Leftrightarrow &-19x
& = &-5\\\Leftrightarrow & \color{red}{-19}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{5}{19} } & & \\ & V = \left\{ \frac{5}{19} \right\} & \\\end{align}\)