Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x-14=15+x\)
- \(x-11=10-x\)
- \(7x+8=1-13x\)
- \(-2x+12=5+x\)
- \(9x+14=5+5x\)
- \(-9x-5=8+x\)
- \(-2x-13=8+x\)
- \(10x-14=1+7x\)
- \(-12x+4=-1+13x\)
- \(-5x+13=-6+x\)
- \(-12x+6=-11+13x\)
- \(6x+9=-9-11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14-x }
& = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 3x \color{blue}{-x }
& = & 15 \color{blue}{+14} \\\Leftrightarrow &2x
& = &29\\\Leftrightarrow & \color{red}{2}x
& = &29\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{29}{2} \\\Leftrightarrow & \color{green}{ x = \frac{29}{2} } & & \\ & V = \left\{ \frac{29}{2} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-11}& = & 10 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+x }
& = & 10 \color{red}{ -x }\color{blue}{+11+x } \\\Leftrightarrow & x \color{blue}{+x }
& = & 10 \color{blue}{+11} \\\Leftrightarrow &2x
& = &21\\\Leftrightarrow & \color{red}{2}x
& = &21\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{21}{2} \\\Leftrightarrow & \color{green}{ x = \frac{21}{2} } & & \\ & V = \left\{ \frac{21}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+8}& = & 1 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+13x }
& = & 1 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & 1 \color{blue}{-8} \\\Leftrightarrow &20x
& = &-7\\\Leftrightarrow & \color{red}{20}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-7}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{20} } & & \\ & V = \left\{ \frac{-7}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x }
& = & 5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 5 \color{blue}{-12} \\\Leftrightarrow &-3x
& = &-7\\\Leftrightarrow & \color{red}{-3}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+14}& = & 5 \color{red}{ +5x } \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14-5x }
& = & 5 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 9x \color{blue}{-5x }
& = & 5 \color{blue}{-14} \\\Leftrightarrow &4x
& = &-9\\\Leftrightarrow & \color{red}{4}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x }
& = & 8 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 8 \color{blue}{+5} \\\Leftrightarrow &-10x
& = &13\\\Leftrightarrow & \color{red}{-10}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{-13}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-13}\color{blue}{+13-x }
& = & 8 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 8 \color{blue}{+13} \\\Leftrightarrow &-3x
& = &21\\\Leftrightarrow & \color{red}{-3}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{21}{-3} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-14}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14-7x }
& = & 1 \color{red}{ +7x }\color{blue}{+14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x }
& = & 1 \color{blue}{+14} \\\Leftrightarrow &3x
& = &15\\\Leftrightarrow & \color{red}{3}x
& = &15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{15}{3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+4}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-13x }
& = & -1 \color{red}{ +13x }\color{blue}{-4-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -1 \color{blue}{-4} \\\Leftrightarrow &-25x
& = &-5\\\Leftrightarrow & \color{red}{-25}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x }
& = & -6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -6 \color{blue}{-13} \\\Leftrightarrow &-6x
& = &-19\\\Leftrightarrow & \color{red}{-6}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+6}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6-13x }
& = & -11 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -11 \color{blue}{-6} \\\Leftrightarrow &-25x
& = &-17\\\Leftrightarrow & \color{red}{-25}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-17}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{17}{25} } & & \\ & V = \left\{ \frac{17}{25} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+9}& = & -9 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9+11x }
& = & -9 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & -9 \color{blue}{-9} \\\Leftrightarrow &17x
& = &-18\\\Leftrightarrow & \color{red}{17}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-18}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{17} } & & \\ & V = \left\{ \frac{-18}{17} \right\} & \\\end{align}\)