Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-13x-13=11+14x\)
- \(3x-1=9-8x\)
- \(-9x-12=-4+x\)
- \(5x-7=10+6x\)
- \(12x+9=-3+7x\)
- \(-14x+12=14+x\)
- \(-6x+6=6+13x\)
- \(-12x+1=-4+13x\)
- \(-7x+15=-9+12x\)
- \(10x+3=-2-3x\)
- \(-4x+2=4+x\)
- \(-4x-13=-1+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -13x \color{red}{-13}& = & 11 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-14x }
& = & 11 \color{red}{ +14x }\color{blue}{+13-14x } \\\Leftrightarrow & -13x \color{blue}{-14x }
& = & 11 \color{blue}{+13} \\\Leftrightarrow &-27x
& = &24\\\Leftrightarrow & \color{red}{-27}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}}
& = & \frac{24}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-1}& = & 9 \color{red}{ -8x } \\\Leftrightarrow & 3x \color{red}{-1}\color{blue}{+1+8x }
& = & 9 \color{red}{ -8x }\color{blue}{+1+8x } \\\Leftrightarrow & 3x \color{blue}{+8x }
& = & 9 \color{blue}{+1} \\\Leftrightarrow &11x
& = &10\\\Leftrightarrow & \color{red}{11}x
& = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x }
& = & -4 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -4 \color{blue}{+12} \\\Leftrightarrow &-10x
& = &8\\\Leftrightarrow & \color{red}{-10}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-7}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7-6x }
& = & 10 \color{red}{ +6x }\color{blue}{+7-6x } \\\Leftrightarrow & 5x \color{blue}{-6x }
& = & 10 \color{blue}{+7} \\\Leftrightarrow &-x
& = &17\\\Leftrightarrow & \color{red}{-}x
& = &17\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{17}{-1} \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+9}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-7x }
& = & -3 \color{red}{ +7x }\color{blue}{-9-7x } \\\Leftrightarrow & 12x \color{blue}{-7x }
& = & -3 \color{blue}{-9} \\\Leftrightarrow &5x
& = &-12\\\Leftrightarrow & \color{red}{5}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+12}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x }
& = & 14 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 14 \color{blue}{-12} \\\Leftrightarrow &-15x
& = &2\\\Leftrightarrow & \color{red}{-15}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+6}& = & 6 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6-13x }
& = & 6 \color{red}{ +13x }\color{blue}{-6-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & 6 \color{blue}{-6} \\\Leftrightarrow &-19x
& = &0\\\Leftrightarrow & \color{red}{-19}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{0}{-19} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+1}& = & -4 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+1}\color{blue}{-1-13x }
& = & -4 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -12x \color{blue}{-13x }
& = & -4 \color{blue}{-1} \\\Leftrightarrow &-25x
& = &-5\\\Leftrightarrow & \color{red}{-25}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}}
& = & \frac{-5}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+15}& = & -9 \color{red}{ +12x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-12x }
& = & -9 \color{red}{ +12x }\color{blue}{-15-12x } \\\Leftrightarrow & -7x \color{blue}{-12x }
& = & -9 \color{blue}{-15} \\\Leftrightarrow &-19x
& = &-24\\\Leftrightarrow & \color{red}{-19}x
& = &-24\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-24}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{24}{19} } & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+3}& = & -2 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3+3x }
& = & -2 \color{red}{ -3x }\color{blue}{-3+3x } \\\Leftrightarrow & 10x \color{blue}{+3x }
& = & -2 \color{blue}{-3} \\\Leftrightarrow &13x
& = &-5\\\Leftrightarrow & \color{red}{13}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x }
& = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & 4 \color{blue}{-2} \\\Leftrightarrow &-5x
& = &2\\\Leftrightarrow & \color{red}{-5}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x }
& = & -1 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -1 \color{blue}{+13} \\\Leftrightarrow &-5x
& = &12\\\Leftrightarrow & \color{red}{-5}x
& = &12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{5} } & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)