Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-5x-7=12+x\)
- \(6x-12=12-5x\)
- \(9x-2=3-13x\)
- \(-9x-14=-8+x\)
- \(14x-15=-5-13x\)
- \(7x-9=4+13x\)
- \(2x-7=15+13x\)
- \(6x+11=7-11x\)
- \(12x+7=-12+x\)
- \(-10x-2=-13+x\)
- \(6x+14=5+x\)
- \(2x-9=-9+9x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -5x \color{red}{-7}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-x }
& = & 12 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 12 \color{blue}{+7} \\\Leftrightarrow &-6x
& = &19\\\Leftrightarrow & \color{red}{-6}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{6} } & & \\ & V = \left\{ \frac{-19}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-12}& = & 12 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+5x }
& = & 12 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & 12 \color{blue}{+12} \\\Leftrightarrow &11x
& = &24\\\Leftrightarrow & \color{red}{11}x
& = &24\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{24}{11} \\\Leftrightarrow & \color{green}{ x = \frac{24}{11} } & & \\ & V = \left\{ \frac{24}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-2}& = & 3 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2+13x }
& = & 3 \color{red}{ -13x }\color{blue}{+2+13x } \\\Leftrightarrow & 9x \color{blue}{+13x }
& = & 3 \color{blue}{+2} \\\Leftrightarrow &22x
& = &5\\\Leftrightarrow & \color{red}{22}x
& = &5\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{5}{22} \\\Leftrightarrow & \color{green}{ x = \frac{5}{22} } & & \\ & V = \left\{ \frac{5}{22} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-14}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x }
& = & -8 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -8 \color{blue}{+14} \\\Leftrightarrow &-10x
& = &6\\\Leftrightarrow & \color{red}{-10}x
& = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{-15}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+13x }
& = & -5 \color{red}{ -13x }\color{blue}{+15+13x } \\\Leftrightarrow & 14x \color{blue}{+13x }
& = & -5 \color{blue}{+15} \\\Leftrightarrow &27x
& = &10\\\Leftrightarrow & \color{red}{27}x
& = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}}
& = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-9}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9-13x }
& = & 4 \color{red}{ +13x }\color{blue}{+9-13x } \\\Leftrightarrow & 7x \color{blue}{-13x }
& = & 4 \color{blue}{+9} \\\Leftrightarrow &-6x
& = &13\\\Leftrightarrow & \color{red}{-6}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-7}& = & 15 \color{red}{ +13x } \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7-13x }
& = & 15 \color{red}{ +13x }\color{blue}{+7-13x } \\\Leftrightarrow & 2x \color{blue}{-13x }
& = & 15 \color{blue}{+7} \\\Leftrightarrow &-11x
& = &22\\\Leftrightarrow & \color{red}{-11}x
& = &22\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{22}{-11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+11}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11+11x }
& = & 7 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 6x \color{blue}{+11x }
& = & 7 \color{blue}{-11} \\\Leftrightarrow &17x
& = &-4\\\Leftrightarrow & \color{red}{17}x
& = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{+7}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-x }
& = & -12 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 12x \color{blue}{-x }
& = & -12 \color{blue}{-7} \\\Leftrightarrow &11x
& = &-19\\\Leftrightarrow & \color{red}{11}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{11} } & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-2}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-x }
& = & -13 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -13 \color{blue}{+2} \\\Leftrightarrow &-11x
& = &-11\\\Leftrightarrow & \color{red}{-11}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+14}& = & 5 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-x }
& = & 5 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 5 \color{blue}{-14} \\\Leftrightarrow &5x
& = &-9\\\Leftrightarrow & \color{red}{5}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{-9}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & 2x \color{red}{-9}\color{blue}{+9-9x }
& = & -9 \color{red}{ +9x }\color{blue}{+9-9x } \\\Leftrightarrow & 2x \color{blue}{-9x }
& = & -9 \color{blue}{+9} \\\Leftrightarrow &-7x
& = &0\\\Leftrightarrow & \color{red}{-7}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{0}{-7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)