Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(11x+13=12+8x\)
- \(-13x-10=-9+x\)
- \(4x+14=-8+7x\)
- \(11x+10=-10+12x\)
- \(11x-13=-12-7x\)
- \(7x-11=4+12x\)
- \(5x-3=10-9x\)
- \(-14x+11=13+x\)
- \(-15x+11=1+x\)
- \(-14x-6=6+x\)
- \(11x+9=-7-13x\)
- \(-5x-9=-15+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 11x \color{red}{+13}& = & 12 \color{red}{ +8x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-8x }
& = & 12 \color{red}{ +8x }\color{blue}{-13-8x } \\\Leftrightarrow & 11x \color{blue}{-8x }
& = & 12 \color{blue}{-13} \\\Leftrightarrow &3x
& = &-1\\\Leftrightarrow & \color{red}{3}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x }
& = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -9 \color{blue}{+10} \\\Leftrightarrow &-14x
& = &1\\\Leftrightarrow & \color{red}{-14}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{14} } & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+14}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14-7x }
& = & -8 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 4x \color{blue}{-7x }
& = & -8 \color{blue}{-14} \\\Leftrightarrow &-3x
& = &-22\\\Leftrightarrow & \color{red}{-3}x
& = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+10}& = & -10 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+10}\color{blue}{-10-12x }
& = & -10 \color{red}{ +12x }\color{blue}{-10-12x } \\\Leftrightarrow & 11x \color{blue}{-12x }
& = & -10 \color{blue}{-10} \\\Leftrightarrow &-x
& = &-20\\\Leftrightarrow & \color{red}{-}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-20}{-1} \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-13}& = & -12 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-13}\color{blue}{+13+7x }
& = & -12 \color{red}{ -7x }\color{blue}{+13+7x } \\\Leftrightarrow & 11x \color{blue}{+7x }
& = & -12 \color{blue}{+13} \\\Leftrightarrow &18x
& = &1\\\Leftrightarrow & \color{red}{18}x
& = &1\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}}
& = & \frac{1}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{18} } & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-11}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11-12x }
& = & 4 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 7x \color{blue}{-12x }
& = & 4 \color{blue}{+11} \\\Leftrightarrow &-5x
& = &15\\\Leftrightarrow & \color{red}{-5}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{15}{-5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-3}& = & 10 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3+9x }
& = & 10 \color{red}{ -9x }\color{blue}{+3+9x } \\\Leftrightarrow & 5x \color{blue}{+9x }
& = & 10 \color{blue}{+3} \\\Leftrightarrow &14x
& = &13\\\Leftrightarrow & \color{red}{14}x
& = &13\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{13}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x }
& = & 13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 13 \color{blue}{-11} \\\Leftrightarrow &-15x
& = &2\\\Leftrightarrow & \color{red}{-15}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x }
& = & 1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 1 \color{blue}{-11} \\\Leftrightarrow &-16x
& = &-10\\\Leftrightarrow & \color{red}{-16}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{5}{8} } & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-6}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x }
& = & 6 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 6 \color{blue}{+6} \\\Leftrightarrow &-15x
& = &12\\\Leftrightarrow & \color{red}{-15}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+9}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+13x }
& = & -7 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 11x \color{blue}{+13x }
& = & -7 \color{blue}{-9} \\\Leftrightarrow &24x
& = &-16\\\Leftrightarrow & \color{red}{24}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}}
& = & \frac{-16}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-9}& = & -15 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-9}\color{blue}{+9-8x }
& = & -15 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & -5x \color{blue}{-8x }
& = & -15 \color{blue}{+9} \\\Leftrightarrow &-13x
& = &-6\\\Leftrightarrow & \color{red}{-13}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)