Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-5x-12=11+6x\)
- \(7x+12=-9-3x\)
- \(-15x+12=-9+8x\)
- \(-10x-11=3+x\)
- \(4x-3=-10+9x\)
- \(13x-3=-15-12x\)
- \(-6x+5=10+7x\)
- \(7x+6=4+2x\)
- \(-15x+9=9+x\)
- \(7x-12=11-6x\)
- \(-10x-1=14+x\)
- \(-14x+15=3+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -5x \color{red}{-12}& = & 11 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-6x }
& = & 11 \color{red}{ +6x }\color{blue}{+12-6x } \\\Leftrightarrow & -5x \color{blue}{-6x }
& = & 11 \color{blue}{+12} \\\Leftrightarrow &-11x
& = &23\\\Leftrightarrow & \color{red}{-11}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+12}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12+3x }
& = & -9 \color{red}{ -3x }\color{blue}{-12+3x } \\\Leftrightarrow & 7x \color{blue}{+3x }
& = & -9 \color{blue}{-12} \\\Leftrightarrow &10x
& = &-21\\\Leftrightarrow & \color{red}{10}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-21}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{10} } & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+12}& = & -9 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-8x }
& = & -9 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & -15x \color{blue}{-8x }
& = & -9 \color{blue}{-12} \\\Leftrightarrow &-23x
& = &-21\\\Leftrightarrow & \color{red}{-23}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-21}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{21}{23} } & & \\ & V = \left\{ \frac{21}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-11}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11-x }
& = & 3 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 3 \color{blue}{+11} \\\Leftrightarrow &-11x
& = &14\\\Leftrightarrow & \color{red}{-11}x
& = &14\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{14}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{11} } & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-3}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3-9x }
& = & -10 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 4x \color{blue}{-9x }
& = & -10 \color{blue}{+3} \\\Leftrightarrow &-5x
& = &-7\\\Leftrightarrow & \color{red}{-5}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 13x \color{red}{-3}& = & -15 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+12x }
& = & -15 \color{red}{ -12x }\color{blue}{+3+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & -15 \color{blue}{+3} \\\Leftrightarrow &25x
& = &-12\\\Leftrightarrow & \color{red}{25}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-12}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{25} } & & \\ & V = \left\{ \frac{-12}{25} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+5}& = & 10 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5-7x }
& = & 10 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & 10 \color{blue}{-5} \\\Leftrightarrow &-13x
& = &5\\\Leftrightarrow & \color{red}{-13}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+6}& = & 4 \color{red}{ +2x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6-2x }
& = & 4 \color{red}{ +2x }\color{blue}{-6-2x } \\\Leftrightarrow & 7x \color{blue}{-2x }
& = & 4 \color{blue}{-6} \\\Leftrightarrow &5x
& = &-2\\\Leftrightarrow & \color{red}{5}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+9}\color{blue}{-9-x }
& = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 9 \color{blue}{-9} \\\Leftrightarrow &-16x
& = &0\\\Leftrightarrow & \color{red}{-16}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{0}{-16} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-12}& = & 11 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12+6x }
& = & 11 \color{red}{ -6x }\color{blue}{+12+6x } \\\Leftrightarrow & 7x \color{blue}{+6x }
& = & 11 \color{blue}{+12} \\\Leftrightarrow &13x
& = &23\\\Leftrightarrow & \color{red}{13}x
& = &23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-1}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1-x }
& = & 14 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 14 \color{blue}{+1} \\\Leftrightarrow &-11x
& = &15\\\Leftrightarrow & \color{red}{-11}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+15}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x }
& = & 3 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 3 \color{blue}{-15} \\\Leftrightarrow &-15x
& = &-12\\\Leftrightarrow & \color{red}{-15}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)