Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-x-14=2-12x\)
- \(-2x-2=11+3x\)
- \(9x+6=-11+13x\)
- \(-11x-11=3+x\)
- \(10x-6=6+7x\)
- \(11x-11=9-2x\)
- \(11x-12=13+5x\)
- \(-3x-11=13+4x\)
- \(5x+13=7+x\)
- \(-13x+15=5+x\)
- \(4x+5=6-15x\)
- \(11x-15=6+14x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -x \color{red}{-14}& = & 2 \color{red}{ -12x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+12x }
& = & 2 \color{red}{ -12x }\color{blue}{+14+12x } \\\Leftrightarrow & -x \color{blue}{+12x }
& = & 2 \color{blue}{+14} \\\Leftrightarrow &11x
& = &16\\\Leftrightarrow & \color{red}{11}x
& = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-2}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-3x }
& = & 11 \color{red}{ +3x }\color{blue}{+2-3x } \\\Leftrightarrow & -2x \color{blue}{-3x }
& = & 11 \color{blue}{+2} \\\Leftrightarrow &-5x
& = &13\\\Leftrightarrow & \color{red}{-5}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+6}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6-13x }
& = & -11 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & 9x \color{blue}{-13x }
& = & -11 \color{blue}{-6} \\\Leftrightarrow &-4x
& = &-17\\\Leftrightarrow & \color{red}{-4}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{-17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x }
& = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 3 \color{blue}{+11} \\\Leftrightarrow &-12x
& = &14\\\Leftrightarrow & \color{red}{-12}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-6}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6-7x }
& = & 6 \color{red}{ +7x }\color{blue}{+6-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & 6 \color{blue}{+6} \\\Leftrightarrow &3x
& = &12\\\Leftrightarrow & \color{red}{3}x
& = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-11}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11+2x }
& = & 9 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & 11x \color{blue}{+2x }
& = & 9 \color{blue}{+11} \\\Leftrightarrow &13x
& = &20\\\Leftrightarrow & \color{red}{13}x
& = &20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-12}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12-5x }
& = & 13 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 11x \color{blue}{-5x }
& = & 13 \color{blue}{+12} \\\Leftrightarrow &6x
& = &25\\\Leftrightarrow & \color{red}{6}x
& = &25\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}}
& = & \frac{25}{6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-11}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-4x }
& = & 13 \color{red}{ +4x }\color{blue}{+11-4x } \\\Leftrightarrow & -3x \color{blue}{-4x }
& = & 13 \color{blue}{+11} \\\Leftrightarrow &-7x
& = &24\\\Leftrightarrow & \color{red}{-7}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{24}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{7} } & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 5x \color{red}{+13}\color{blue}{-13-x }
& = & 7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 5x \color{blue}{-x }
& = & 7 \color{blue}{-13} \\\Leftrightarrow &4x
& = &-6\\\Leftrightarrow & \color{red}{4}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{+15}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15-x }
& = & 5 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 5 \color{blue}{-15} \\\Leftrightarrow &-14x
& = &-10\\\Leftrightarrow & \color{red}{-14}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+5}& = & 6 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+15x }
& = & 6 \color{red}{ -15x }\color{blue}{-5+15x } \\\Leftrightarrow & 4x \color{blue}{+15x }
& = & 6 \color{blue}{-5} \\\Leftrightarrow &19x
& = &1\\\Leftrightarrow & \color{red}{19}x
& = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-15}& = & 6 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15-14x }
& = & 6 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & 11x \color{blue}{-14x }
& = & 6 \color{blue}{+15} \\\Leftrightarrow &-3x
& = &21\\\Leftrightarrow & \color{red}{-3}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)