Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x-11=13+x\)
- \(-6x-12=2+13x\)
- \(-6x-13=5+x\)
- \(4x+3=-3+x\)
- \(2x-4=-9+x\)
- \(-10x+5=8+x\)
- \(-14x-6=-13+x\)
- \(-8x+11=-5+x\)
- \(-4x+5=-7+x\)
- \(13x+7=-6+2x\)
- \(-7x-13=-11+x\)
- \(15x-1=-3+11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{-11}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x }
& = & 13 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 13 \color{blue}{+11} \\\Leftrightarrow &-10x
& = &24\\\Leftrightarrow & \color{red}{-10}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-12}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12-13x }
& = & 2 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & 2 \color{blue}{+12} \\\Leftrightarrow &-19x
& = &14\\\Leftrightarrow & \color{red}{-19}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{14}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{19} } & & \\ & V = \left\{ \frac{-14}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-13}\color{blue}{+13-x }
& = & 5 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 5 \color{blue}{+13} \\\Leftrightarrow &-7x
& = &18\\\Leftrightarrow & \color{red}{-7}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+3}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-x }
& = & -3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & 4x \color{blue}{-x }
& = & -3 \color{blue}{-3} \\\Leftrightarrow &3x
& = &-6\\\Leftrightarrow & \color{red}{3}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}}
& = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-4}& = & -9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4-x }
& = & -9 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & -9 \color{blue}{+4} \\\Leftrightarrow &x
& = &-5\\\Leftrightarrow & \color{red}{}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+5}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5-x }
& = & 8 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 8 \color{blue}{-5} \\\Leftrightarrow &-11x
& = &3\\\Leftrightarrow & \color{red}{-11}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6-x }
& = & -13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -13 \color{blue}{+6} \\\Leftrightarrow &-15x
& = &-7\\\Leftrightarrow & \color{red}{-15}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+11}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x }
& = & -5 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & -5 \color{blue}{-11} \\\Leftrightarrow &-9x
& = &-16\\\Leftrightarrow & \color{red}{-9}x
& = &-16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+5}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+5}\color{blue}{-5-x }
& = & -7 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -7 \color{blue}{-5} \\\Leftrightarrow &-5x
& = &-12\\\Leftrightarrow & \color{red}{-5}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{+7}& = & -6 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7-2x }
& = & -6 \color{red}{ +2x }\color{blue}{-7-2x } \\\Leftrightarrow & 13x \color{blue}{-2x }
& = & -6 \color{blue}{-7} \\\Leftrightarrow &11x
& = &-13\\\Leftrightarrow & \color{red}{11}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-13}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{11} } & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-13}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-13}\color{blue}{+13-x }
& = & -11 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -11 \color{blue}{+13} \\\Leftrightarrow &-8x
& = &2\\\Leftrightarrow & \color{red}{-8}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{2}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-1}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-11x }
& = & -3 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 15x \color{blue}{-11x }
& = & -3 \color{blue}{+1} \\\Leftrightarrow &4x
& = &-2\\\Leftrightarrow & \color{red}{4}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}}
& = & \frac{-2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)