Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x-6=-1+x\)
- \(-5x+15=-10+x\)
- \(-13x-9=13+x\)
- \(11x-14=6+x\)
- \(2x+14=9+13x\)
- \(-11x+1=2+x\)
- \(-15x-3=-2+x\)
- \(-8x+7=12+x\)
- \(7x-14=-3-10x\)
- \(-12x-5=-1+x\)
- \(6x-2=12+x\)
- \(-5x+10=3+8x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{-6}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-x }
& = & -1 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -1 \color{blue}{+6} \\\Leftrightarrow &-10x
& = &5\\\Leftrightarrow & \color{red}{-10}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+15}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15-x }
& = & -10 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & -10 \color{blue}{-15} \\\Leftrightarrow &-6x
& = &-25\\\Leftrightarrow & \color{red}{-6}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-9}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x }
& = & 13 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & 13 \color{blue}{+9} \\\Leftrightarrow &-14x
& = &22\\\Leftrightarrow & \color{red}{-14}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-14}\color{blue}{+14-x }
& = & 6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & 11x \color{blue}{-x }
& = & 6 \color{blue}{+14} \\\Leftrightarrow &10x
& = &20\\\Leftrightarrow & \color{red}{10}x
& = &20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{20}{10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+14}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{+14}\color{blue}{-14-13x }
& = & 9 \color{red}{ +13x }\color{blue}{-14-13x } \\\Leftrightarrow & 2x \color{blue}{-13x }
& = & 9 \color{blue}{-14} \\\Leftrightarrow &-11x
& = &-5\\\Leftrightarrow & \color{red}{-11}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1-x }
& = & 2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 2 \color{blue}{-1} \\\Leftrightarrow &-12x
& = &1\\\Leftrightarrow & \color{red}{-12}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
- \(\begin{align} & -15x \color{red}{-3}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-x }
& = & -2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -15x \color{blue}{-x }
& = & -2 \color{blue}{+3} \\\Leftrightarrow &-16x
& = &1\\\Leftrightarrow & \color{red}{-16}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x }
& = & 12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 12 \color{blue}{-7} \\\Leftrightarrow &-9x
& = &5\\\Leftrightarrow & \color{red}{-9}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{9} } & & \\ & V = \left\{ \frac{-5}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-14}& = & -3 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+10x }
& = & -3 \color{red}{ -10x }\color{blue}{+14+10x } \\\Leftrightarrow & 7x \color{blue}{+10x }
& = & -3 \color{blue}{+14} \\\Leftrightarrow &17x
& = &11\\\Leftrightarrow & \color{red}{17}x
& = &11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{11}{17} } & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5-x }
& = & -1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -1 \color{blue}{+5} \\\Leftrightarrow &-13x
& = &4\\\Leftrightarrow & \color{red}{-13}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-2}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-x }
& = & 12 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 12 \color{blue}{+2} \\\Leftrightarrow &5x
& = &14\\\Leftrightarrow & \color{red}{5}x
& = &14\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{14}{5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+10}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10-8x }
& = & 3 \color{red}{ +8x }\color{blue}{-10-8x } \\\Leftrightarrow & -5x \color{blue}{-8x }
& = & 3 \color{blue}{-10} \\\Leftrightarrow &-13x
& = &-7\\\Leftrightarrow & \color{red}{-13}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)