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