Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(3x-5=-5-2x\)
- \(12x-1=3-11x\)
- \(-2x+5=8+7x\)
- \(9x-6=6-8x\)
- \(-8x+9=-15+9x\)
- \(5x-1=15-12x\)
- \(-10x-7=5+x\)
- \(12x-1=12-7x\)
- \(-x-7=-8+12x\)
- \(12x-1=-3+x\)
- \(-9x+5=-15+14x\)
- \(-x-13=-5+4x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 3x \color{red}{-5}& = & -5 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+2x }
& = & -5 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 3x \color{blue}{+2x }
& = & -5 \color{blue}{+5} \\\Leftrightarrow &5x
& = &0\\\Leftrightarrow & \color{red}{5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-1}& = & 3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1+11x }
& = & 3 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 3 \color{blue}{+1} \\\Leftrightarrow &23x
& = &4\\\Leftrightarrow & \color{red}{23}x
& = &4\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{4}{23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -2x \color{red}{+5}& = & 8 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-7x }
& = & 8 \color{red}{ +7x }\color{blue}{-5-7x } \\\Leftrightarrow & -2x \color{blue}{-7x }
& = & 8 \color{blue}{-5} \\\Leftrightarrow &-9x
& = &3\\\Leftrightarrow & \color{red}{-9}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{3}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-6}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 9x \color{red}{-6}\color{blue}{+6+8x }
& = & 6 \color{red}{ -8x }\color{blue}{+6+8x } \\\Leftrightarrow & 9x \color{blue}{+8x }
& = & 6 \color{blue}{+6} \\\Leftrightarrow &17x
& = &12\\\Leftrightarrow & \color{red}{17}x
& = &12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{12}{17} } & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+9}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+9}\color{blue}{-9-9x }
& = & -15 \color{red}{ +9x }\color{blue}{-9-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -15 \color{blue}{-9} \\\Leftrightarrow &-17x
& = &-24\\\Leftrightarrow & \color{red}{-17}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-24}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{24}{17} } & & \\ & V = \left\{ \frac{24}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-1}& = & 15 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-1}\color{blue}{+1+12x }
& = & 15 \color{red}{ -12x }\color{blue}{+1+12x } \\\Leftrightarrow & 5x \color{blue}{+12x }
& = & 15 \color{blue}{+1} \\\Leftrightarrow &17x
& = &16\\\Leftrightarrow & \color{red}{17}x
& = &16\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{16}{17} \\\Leftrightarrow & \color{green}{ x = \frac{16}{17} } & & \\ & V = \left\{ \frac{16}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7-x }
& = & 5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 5 \color{blue}{+7} \\\Leftrightarrow &-11x
& = &12\\\Leftrightarrow & \color{red}{-11}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-1}& = & 12 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1+7x }
& = & 12 \color{red}{ -7x }\color{blue}{+1+7x } \\\Leftrightarrow & 12x \color{blue}{+7x }
& = & 12 \color{blue}{+1} \\\Leftrightarrow &19x
& = &13\\\Leftrightarrow & \color{red}{19}x
& = &13\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{13}{19} \\\Leftrightarrow & \color{green}{ x = \frac{13}{19} } & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-7}& = & -8 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{-7}\color{blue}{+7-12x }
& = & -8 \color{red}{ +12x }\color{blue}{+7-12x } \\\Leftrightarrow & -x \color{blue}{-12x }
& = & -8 \color{blue}{+7} \\\Leftrightarrow &-13x
& = &-1\\\Leftrightarrow & \color{red}{-13}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-1}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1-x }
& = & -3 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -3 \color{blue}{+1} \\\Leftrightarrow &11x
& = &-2\\\Leftrightarrow & \color{red}{11}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+5}& = & -15 \color{red}{ +14x } \\\Leftrightarrow & -9x \color{red}{+5}\color{blue}{-5-14x }
& = & -15 \color{red}{ +14x }\color{blue}{-5-14x } \\\Leftrightarrow & -9x \color{blue}{-14x }
& = & -15 \color{blue}{-5} \\\Leftrightarrow &-23x
& = &-20\\\Leftrightarrow & \color{red}{-23}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{-20}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{20}{23} } & & \\ & V = \left\{ \frac{20}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-13}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13-4x }
& = & -5 \color{red}{ +4x }\color{blue}{+13-4x } \\\Leftrightarrow & -x \color{blue}{-4x }
& = & -5 \color{blue}{+13} \\\Leftrightarrow &-5x
& = &8\\\Leftrightarrow & \color{red}{-5}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)