Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-11x-13=-7+x\)
- \(12x-5=-3+x\)
- \(-3x+5=-13+7x\)
- \(-9x+13=-2+x\)
- \(-15x+4=-13+x\)
- \(-12x+12=1+x\)
- \(-13x-8=12+9x\)
- \(-11x-6=-13+6x\)
- \(10x-13=-12+11x\)
- \(-4x+6=13+13x\)
- \(10x-8=5-3x\)
- \(-6x+6=3+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -11x \color{red}{-13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13-x }
& = & -7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & -7 \color{blue}{+13} \\\Leftrightarrow &-12x
& = &6\\\Leftrightarrow & \color{red}{-12}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{6}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-5}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-5}\color{blue}{+5-x }
& = & -3 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -3 \color{blue}{+5} \\\Leftrightarrow &11x
& = &2\\\Leftrightarrow & \color{red}{11}x
& = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+5}& = & -13 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{+5}\color{blue}{-5-7x }
& = & -13 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & -13 \color{blue}{-5} \\\Leftrightarrow &-10x
& = &-18\\\Leftrightarrow & \color{red}{-10}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+13}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13-x }
& = & -2 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -2 \color{blue}{-13} \\\Leftrightarrow &-10x
& = &-15\\\Leftrightarrow & \color{red}{-10}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+4}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x }
& = & -13 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -13 \color{blue}{-4} \\\Leftrightarrow &-16x
& = &-17\\\Leftrightarrow & \color{red}{-16}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-17}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{17}{16} } & & \\ & V = \left\{ \frac{17}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+12}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12-x }
& = & 1 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 1 \color{blue}{-12} \\\Leftrightarrow &-13x
& = &-11\\\Leftrightarrow & \color{red}{-13}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-8}& = & 12 \color{red}{ +9x } \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8-9x }
& = & 12 \color{red}{ +9x }\color{blue}{+8-9x } \\\Leftrightarrow & -13x \color{blue}{-9x }
& = & 12 \color{blue}{+8} \\\Leftrightarrow &-22x
& = &20\\\Leftrightarrow & \color{red}{-22}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}}
& = & \frac{20}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-6}& = & -13 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{-6}\color{blue}{+6-6x }
& = & -13 \color{red}{ +6x }\color{blue}{+6-6x } \\\Leftrightarrow & -11x \color{blue}{-6x }
& = & -13 \color{blue}{+6} \\\Leftrightarrow &-17x
& = &-7\\\Leftrightarrow & \color{red}{-17}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{7}{17} } & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-13}& = & -12 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{-13}\color{blue}{+13-11x }
& = & -12 \color{red}{ +11x }\color{blue}{+13-11x } \\\Leftrightarrow & 10x \color{blue}{-11x }
& = & -12 \color{blue}{+13} \\\Leftrightarrow &-x
& = &1\\\Leftrightarrow & \color{red}{-}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+6}& = & 13 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{+6}\color{blue}{-6-13x }
& = & 13 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -4x \color{blue}{-13x }
& = & 13 \color{blue}{-6} \\\Leftrightarrow &-17x
& = &7\\\Leftrightarrow & \color{red}{-17}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{7}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-8}& = & 5 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8+3x }
& = & 5 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 10x \color{blue}{+3x }
& = & 5 \color{blue}{+8} \\\Leftrightarrow &13x
& = &13\\\Leftrightarrow & \color{red}{13}x
& = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+6}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-13x }
& = & 3 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & 3 \color{blue}{-6} \\\Leftrightarrow &-19x
& = &-3\\\Leftrightarrow & \color{red}{-19}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-3}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{3}{19} } & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)