Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-10x+1=-4+x\)
- \(-9x-5=7+x\)
- \(15x+14=-13-11x\)
- \(-6x+11=-4+x\)
- \(2x-10=9+11x\)
- \(11x+11=10-10x\)
- \(6x-9=4-11x\)
- \(-9x-3=10+x\)
- \(7x-3=14-13x\)
- \(-3x-11=-3+7x\)
- \(x+2=-11+6x\)
- \(-12x+13=-6+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -10x \color{red}{+1}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-x }
& = & -4 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -4 \color{blue}{-1} \\\Leftrightarrow &-11x
& = &-5\\\Leftrightarrow & \color{red}{-11}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-x }
& = & 7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 7 \color{blue}{+5} \\\Leftrightarrow &-10x
& = &12\\\Leftrightarrow & \color{red}{-10}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+14}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14+11x }
& = & -13 \color{red}{ -11x }\color{blue}{-14+11x } \\\Leftrightarrow & 15x \color{blue}{+11x }
& = & -13 \color{blue}{-14} \\\Leftrightarrow &26x
& = &-27\\\Leftrightarrow & \color{red}{26}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}}
& = & \frac{-27}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{26} } & & \\ & V = \left\{ \frac{-27}{26} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+11}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-x }
& = & -4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -4 \color{blue}{-11} \\\Leftrightarrow &-7x
& = &-15\\\Leftrightarrow & \color{red}{-7}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-15}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-10}& = & 9 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-11x }
& = & 9 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & 2x \color{blue}{-11x }
& = & 9 \color{blue}{+10} \\\Leftrightarrow &-9x
& = &19\\\Leftrightarrow & \color{red}{-9}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{19}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{9} } & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+11}& = & 10 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+11}\color{blue}{-11+10x }
& = & 10 \color{red}{ -10x }\color{blue}{-11+10x } \\\Leftrightarrow & 11x \color{blue}{+10x }
& = & 10 \color{blue}{-11} \\\Leftrightarrow &21x
& = &-1\\\Leftrightarrow & \color{red}{21}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{-1}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{21} } & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-9}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-9}\color{blue}{+9+11x }
& = & 4 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 4 \color{blue}{+9} \\\Leftrightarrow &17x
& = &13\\\Leftrightarrow & \color{red}{17}x
& = &13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{13}{17} } & & \\ & V = \left\{ \frac{13}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-3}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3-x }
& = & 10 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 10 \color{blue}{+3} \\\Leftrightarrow &-10x
& = &13\\\Leftrightarrow & \color{red}{-10}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-3}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3+13x }
& = & 14 \color{red}{ -13x }\color{blue}{+3+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & 14 \color{blue}{+3} \\\Leftrightarrow &20x
& = &17\\\Leftrightarrow & \color{red}{20}x
& = &17\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{17}{20} \\\Leftrightarrow & \color{green}{ x = \frac{17}{20} } & & \\ & V = \left\{ \frac{17}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-11}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11-7x }
& = & -3 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & -3x \color{blue}{-7x }
& = & -3 \color{blue}{+11} \\\Leftrightarrow &-10x
& = &8\\\Leftrightarrow & \color{red}{-10}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+2}& = & -11 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2-6x }
& = & -11 \color{red}{ +6x }\color{blue}{-2-6x } \\\Leftrightarrow & x \color{blue}{-6x }
& = & -11 \color{blue}{-2} \\\Leftrightarrow &-5x
& = &-13\\\Leftrightarrow & \color{red}{-5}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+13}& = & -6 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-13x }
& = & -6 \color{red}{ +13x }\color{blue}{-13-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -6 \color{blue}{-13} \\\Leftrightarrow &-25x
& = &-19\\\Leftrightarrow & \color{red}{-25}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-19}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{19}{25} } & & \\ & V = \left\{ \frac{19}{25} \right\} & \\\end{align}\)