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