Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-10x-10=11+x\)
- \(8x-13=10+x\)
- \(-11x-3=13+x\)
- \(-3x+7=-6+4x\)
- \(-2x+12=-15+3x\)
- \(-5x-6=-8+x\)
- \(4x+11=13-15x\)
- \(x-14=-11+12x\)
- \(9x+6=-3-4x\)
- \(10x+5=-10+13x\)
- \(-5x-5=10+x\)
- \(-12x-6=3+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -10x \color{red}{-10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x }
& = & 11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 11 \color{blue}{+10} \\\Leftrightarrow &-11x
& = &21\\\Leftrightarrow & \color{red}{-11}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13-x }
& = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & 10 \color{blue}{+13} \\\Leftrightarrow &7x
& = &23\\\Leftrightarrow & \color{red}{7}x
& = &23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-3}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3-x }
& = & 13 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 13 \color{blue}{+3} \\\Leftrightarrow &-12x
& = &16\\\Leftrightarrow & \color{red}{-12}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+7}& = & -6 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+7}\color{blue}{-7-4x }
& = & -6 \color{red}{ +4x }\color{blue}{-7-4x } \\\Leftrightarrow & -3x \color{blue}{-4x }
& = & -6 \color{blue}{-7} \\\Leftrightarrow &-7x
& = &-13\\\Leftrightarrow & \color{red}{-7}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+12}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-3x }
& = & -15 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & -2x \color{blue}{-3x }
& = & -15 \color{blue}{-12} \\\Leftrightarrow &-5x
& = &-27\\\Leftrightarrow & \color{red}{-5}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{27}{5} } & & \\ & V = \left\{ \frac{27}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-6}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-6}\color{blue}{+6-x }
& = & -8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -8 \color{blue}{+6} \\\Leftrightarrow &-6x
& = &-2\\\Leftrightarrow & \color{red}{-6}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-2}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{+11}& = & 13 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11+15x }
& = & 13 \color{red}{ -15x }\color{blue}{-11+15x } \\\Leftrightarrow & 4x \color{blue}{+15x }
& = & 13 \color{blue}{-11} \\\Leftrightarrow &19x
& = &2\\\Leftrightarrow & \color{red}{19}x
& = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-14}& = & -11 \color{red}{ +12x } \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14-12x }
& = & -11 \color{red}{ +12x }\color{blue}{+14-12x } \\\Leftrightarrow & x \color{blue}{-12x }
& = & -11 \color{blue}{+14} \\\Leftrightarrow &-11x
& = &3\\\Leftrightarrow & \color{red}{-11}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+6}& = & -3 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+6}\color{blue}{-6+4x }
& = & -3 \color{red}{ -4x }\color{blue}{-6+4x } \\\Leftrightarrow & 9x \color{blue}{+4x }
& = & -3 \color{blue}{-6} \\\Leftrightarrow &13x
& = &-9\\\Leftrightarrow & \color{red}{13}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+5}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5-13x }
& = & -10 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & 10x \color{blue}{-13x }
& = & -10 \color{blue}{-5} \\\Leftrightarrow &-3x
& = &-15\\\Leftrightarrow & \color{red}{-3}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-15}{-3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-5}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x }
& = & 10 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 10 \color{blue}{+5} \\\Leftrightarrow &-6x
& = &15\\\Leftrightarrow & \color{red}{-6}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-6}& = & 3 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-13x }
& = & 3 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & 3 \color{blue}{+6} \\\Leftrightarrow &-25x
& = &9\\\Leftrightarrow & \color{red}{-25}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{9}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{25} } & & \\ & V = \left\{ \frac{-9}{25} \right\} & \\\end{align}\)