Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(13x+13=3-12x\)
- \(12x-7=15-7x\)
- \(12x-6=-8+13x\)
- \(5x-14=11-14x\)
- \(7x-15=1-2x\)
- \(-12x+13=5+x\)
- \(-6x+15=-10+7x\)
- \(-7x-10=5+11x\)
- \(-10x+14=6+x\)
- \(3x-4=-8+10x\)
- \(6x-15=10+11x\)
- \(2x-15=9+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 13x \color{red}{+13}& = & 3 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13+12x }
& = & 3 \color{red}{ -12x }\color{blue}{-13+12x } \\\Leftrightarrow & 13x \color{blue}{+12x }
& = & 3 \color{blue}{-13} \\\Leftrightarrow &25x
& = &-10\\\Leftrightarrow & \color{red}{25}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}}
& = & \frac{-10}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-7}& = & 15 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+7x }
& = & 15 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 12x \color{blue}{+7x }
& = & 15 \color{blue}{+7} \\\Leftrightarrow &19x
& = &22\\\Leftrightarrow & \color{red}{19}x
& = &22\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{22}{19} \\\Leftrightarrow & \color{green}{ x = \frac{22}{19} } & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-6}& = & -8 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6-13x }
& = & -8 \color{red}{ +13x }\color{blue}{+6-13x } \\\Leftrightarrow & 12x \color{blue}{-13x }
& = & -8 \color{blue}{+6} \\\Leftrightarrow &-x
& = &-2\\\Leftrightarrow & \color{red}{-}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-14}& = & 11 \color{red}{ -14x } \\\Leftrightarrow & 5x \color{red}{-14}\color{blue}{+14+14x }
& = & 11 \color{red}{ -14x }\color{blue}{+14+14x } \\\Leftrightarrow & 5x \color{blue}{+14x }
& = & 11 \color{blue}{+14} \\\Leftrightarrow &19x
& = &25\\\Leftrightarrow & \color{red}{19}x
& = &25\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{25}{19} \\\Leftrightarrow & \color{green}{ x = \frac{25}{19} } & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-15}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15+2x }
& = & 1 \color{red}{ -2x }\color{blue}{+15+2x } \\\Leftrightarrow & 7x \color{blue}{+2x }
& = & 1 \color{blue}{+15} \\\Leftrightarrow &9x
& = &16\\\Leftrightarrow & \color{red}{9}x
& = &16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{16}{9} } & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+13}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13-x }
& = & 5 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 5 \color{blue}{-13} \\\Leftrightarrow &-13x
& = &-8\\\Leftrightarrow & \color{red}{-13}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+15}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-7x }
& = & -10 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x }
& = & -10 \color{blue}{-15} \\\Leftrightarrow &-13x
& = &-25\\\Leftrightarrow & \color{red}{-13}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-10}& = & 5 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-11x }
& = & 5 \color{red}{ +11x }\color{blue}{+10-11x } \\\Leftrightarrow & -7x \color{blue}{-11x }
& = & 5 \color{blue}{+10} \\\Leftrightarrow &-18x
& = &15\\\Leftrightarrow & \color{red}{-18}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{15}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14-x }
& = & 6 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 6 \color{blue}{-14} \\\Leftrightarrow &-11x
& = &-8\\\Leftrightarrow & \color{red}{-11}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-4}& = & -8 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4-10x }
& = & -8 \color{red}{ +10x }\color{blue}{+4-10x } \\\Leftrightarrow & 3x \color{blue}{-10x }
& = & -8 \color{blue}{+4} \\\Leftrightarrow &-7x
& = &-4\\\Leftrightarrow & \color{red}{-7}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-15}& = & 10 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15-11x }
& = & 10 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 6x \color{blue}{-11x }
& = & 10 \color{blue}{+15} \\\Leftrightarrow &-5x
& = &25\\\Leftrightarrow & \color{red}{-5}x
& = &25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{25}{-5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-15}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15-x }
& = & 9 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 9 \color{blue}{+15} \\\Leftrightarrow &x
& = &24\\\Leftrightarrow & \color{red}{}x
& = &24\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & 24 \\\Leftrightarrow & \color{green}{ x = 24 } & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)