Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-8x+11=-10+9x\)
- \(-5x-5=-11+x\)
- \(5x-9=-11-14x\)
- \(9x-13=-7+7x\)
- \(x+9=-6-13x\)
- \(-12x-12=10+x\)
- \(x+14=-12+12x\)
- \(8x-11=8+5x\)
- \(9x-4=-13+4x\)
- \(12x-10=6+x\)
- \(15x+2=-2+7x\)
- \(-10x-10=13+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -8x \color{red}{+11}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-9x }
& = & -10 \color{red}{ +9x }\color{blue}{-11-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -10 \color{blue}{-11} \\\Leftrightarrow &-17x
& = &-21\\\Leftrightarrow & \color{red}{-17}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-21}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{21}{17} } & & \\ & V = \left\{ \frac{21}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x }
& = & -11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -11 \color{blue}{+5} \\\Leftrightarrow &-6x
& = &-6\\\Leftrightarrow & \color{red}{-6}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-9}& = & -11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9+14x }
& = & -11 \color{red}{ -14x }\color{blue}{+9+14x } \\\Leftrightarrow & 5x \color{blue}{+14x }
& = & -11 \color{blue}{+9} \\\Leftrightarrow &19x
& = &-2\\\Leftrightarrow & \color{red}{19}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{19} } & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-13}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-13}\color{blue}{+13-7x }
& = & -7 \color{red}{ +7x }\color{blue}{+13-7x } \\\Leftrightarrow & 9x \color{blue}{-7x }
& = & -7 \color{blue}{+13} \\\Leftrightarrow &2x
& = &6\\\Leftrightarrow & \color{red}{2}x
& = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}}
& = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+9}& = & -6 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9+13x }
& = & -6 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & x \color{blue}{+13x }
& = & -6 \color{blue}{-9} \\\Leftrightarrow &14x
& = &-15\\\Leftrightarrow & \color{red}{14}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-12}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12-x }
& = & 10 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 10 \color{blue}{+12} \\\Leftrightarrow &-13x
& = &22\\\Leftrightarrow & \color{red}{-13}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{13} } & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{+14}& = & -12 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14-12x }
& = & -12 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & x \color{blue}{-12x }
& = & -12 \color{blue}{-14} \\\Leftrightarrow &-11x
& = &-26\\\Leftrightarrow & \color{red}{-11}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-11}& = & 8 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-11}\color{blue}{+11-5x }
& = & 8 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 8x \color{blue}{-5x }
& = & 8 \color{blue}{+11} \\\Leftrightarrow &3x
& = &19\\\Leftrightarrow & \color{red}{3}x
& = &19\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{19}{3} \\\Leftrightarrow & \color{green}{ x = \frac{19}{3} } & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-4}& = & -13 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4-4x }
& = & -13 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 9x \color{blue}{-4x }
& = & -13 \color{blue}{+4} \\\Leftrightarrow &5x
& = &-9\\\Leftrightarrow & \color{red}{5}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10-x }
& = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & 6 \color{blue}{+10} \\\Leftrightarrow &11x
& = &16\\\Leftrightarrow & \color{red}{11}x
& = &16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+2}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2-7x }
& = & -2 \color{red}{ +7x }\color{blue}{-2-7x } \\\Leftrightarrow & 15x \color{blue}{-7x }
& = & -2 \color{blue}{-2} \\\Leftrightarrow &8x
& = &-4\\\Leftrightarrow & \color{red}{8}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-10}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x }
& = & 13 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 13 \color{blue}{+10} \\\Leftrightarrow &-11x
& = &23\\\Leftrightarrow & \color{red}{-11}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)