Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-7x+15=-13+8x\)
- \(-10x-8=14+11x\)
- \(7x-7=14+8x\)
- \(-15x-1=9+x\)
- \(8x-10=14+9x\)
- \(-11x-4=5+x\)
- \(-6x+13=-1+7x\)
- \(14x+13=-6+x\)
- \(5x+9=14-4x\)
- \(14x+10=-15+5x\)
- \(-15x-8=-4+8x\)
- \(8x+13=15-15x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -7x \color{red}{+15}& = & -13 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-8x }
& = & -13 \color{red}{ +8x }\color{blue}{-15-8x } \\\Leftrightarrow & -7x \color{blue}{-8x }
& = & -13 \color{blue}{-15} \\\Leftrightarrow &-15x
& = &-28\\\Leftrightarrow & \color{red}{-15}x
& = &-28\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-28}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{28}{15} } & & \\ & V = \left\{ \frac{28}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-8}& = & 14 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8-11x }
& = & 14 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -10x \color{blue}{-11x }
& = & 14 \color{blue}{+8} \\\Leftrightarrow &-21x
& = &22\\\Leftrightarrow & \color{red}{-21}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}}
& = & \frac{22}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{21} } & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-7}& = & 14 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7-8x }
& = & 14 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & 7x \color{blue}{-8x }
& = & 14 \color{blue}{+7} \\\Leftrightarrow &-x
& = &21\\\Leftrightarrow & \color{red}{-}x
& = &21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{21}{-1} \\\Leftrightarrow & \color{green}{ x = -21 } & & \\ & V = \left\{ -21 \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1-x }
& = & 9 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & 9 \color{blue}{+1} \\\Leftrightarrow &-16x
& = &10\\\Leftrightarrow & \color{red}{-16}x
& = &10\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{10}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{-10}& = & 14 \color{red}{ +9x } \\\Leftrightarrow & 8x \color{red}{-10}\color{blue}{+10-9x }
& = & 14 \color{red}{ +9x }\color{blue}{+10-9x } \\\Leftrightarrow & 8x \color{blue}{-9x }
& = & 14 \color{blue}{+10} \\\Leftrightarrow &-x
& = &24\\\Leftrightarrow & \color{red}{-}x
& = &24\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{24}{-1} \\\Leftrightarrow & \color{green}{ x = -24 } & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{-4}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x }
& = & 5 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 5 \color{blue}{+4} \\\Leftrightarrow &-12x
& = &9\\\Leftrightarrow & \color{red}{-12}x
& = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+13}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13-7x }
& = & -1 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -1 \color{blue}{-13} \\\Leftrightarrow &-13x
& = &-14\\\Leftrightarrow & \color{red}{-13}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-14}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{14}{13} } & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+13}& = & -6 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+13}\color{blue}{-13-x }
& = & -6 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -6 \color{blue}{-13} \\\Leftrightarrow &13x
& = &-19\\\Leftrightarrow & \color{red}{13}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+9}& = & 14 \color{red}{ -4x } \\\Leftrightarrow & 5x \color{red}{+9}\color{blue}{-9+4x }
& = & 14 \color{red}{ -4x }\color{blue}{-9+4x } \\\Leftrightarrow & 5x \color{blue}{+4x }
& = & 14 \color{blue}{-9} \\\Leftrightarrow &9x
& = &5\\\Leftrightarrow & \color{red}{9}x
& = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+10}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10-5x }
& = & -15 \color{red}{ +5x }\color{blue}{-10-5x } \\\Leftrightarrow & 14x \color{blue}{-5x }
& = & -15 \color{blue}{-10} \\\Leftrightarrow &9x
& = &-25\\\Leftrightarrow & \color{red}{9}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-25}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-8}& = & -4 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-8x }
& = & -4 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & -15x \color{blue}{-8x }
& = & -4 \color{blue}{+8} \\\Leftrightarrow &-23x
& = &4\\\Leftrightarrow & \color{red}{-23}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}}
& = & \frac{4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+13}& = & 15 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+13}\color{blue}{-13+15x }
& = & 15 \color{red}{ -15x }\color{blue}{-13+15x } \\\Leftrightarrow & 8x \color{blue}{+15x }
& = & 15 \color{blue}{-13} \\\Leftrightarrow &23x
& = &2\\\Leftrightarrow & \color{red}{23}x
& = &2\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{2}{23} \\\Leftrightarrow & \color{green}{ x = \frac{2}{23} } & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)