Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(5x-2=3+9x\)
- \(12x-12=-12+7x\)
- \(x-11=15-13x\)
- \(-6x-2=-1+x\)
- \(8x+6=1+x\)
- \(-6x+8=-10+x\)
- \(7x+8=11-10x\)
- \(12x-9=13-11x\)
- \(9x+12=-7+14x\)
- \(7x-12=11+8x\)
- \(-7x+14=-12+x\)
- \(-6x+11=-10+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 5x \color{red}{-2}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2-9x }
& = & 3 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 5x \color{blue}{-9x }
& = & 3 \color{blue}{+2} \\\Leftrightarrow &-4x
& = &5\\\Leftrightarrow & \color{red}{-4}x
& = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-12}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12-7x }
& = & -12 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 12x \color{blue}{-7x }
& = & -12 \color{blue}{+12} \\\Leftrightarrow &5x
& = &0\\\Leftrightarrow & \color{red}{5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-11}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+13x }
& = & 15 \color{red}{ -13x }\color{blue}{+11+13x } \\\Leftrightarrow & x \color{blue}{+13x }
& = & 15 \color{blue}{+11} \\\Leftrightarrow &14x
& = &26\\\Leftrightarrow & \color{red}{14}x
& = &26\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{26}{14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2-x }
& = & -1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -1 \color{blue}{+2} \\\Leftrightarrow &-7x
& = &1\\\Leftrightarrow & \color{red}{-7}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+6}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x }
& = & 1 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x }
& = & 1 \color{blue}{-6} \\\Leftrightarrow &7x
& = &-5\\\Leftrightarrow & \color{red}{7}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{-5}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+8}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-x }
& = & -10 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -10 \color{blue}{-8} \\\Leftrightarrow &-7x
& = &-18\\\Leftrightarrow & \color{red}{-7}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+8}& = & 11 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8+10x }
& = & 11 \color{red}{ -10x }\color{blue}{-8+10x } \\\Leftrightarrow & 7x \color{blue}{+10x }
& = & 11 \color{blue}{-8} \\\Leftrightarrow &17x
& = &3\\\Leftrightarrow & \color{red}{17}x
& = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-9}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+11x }
& = & 13 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 13 \color{blue}{+9} \\\Leftrightarrow &23x
& = &22\\\Leftrightarrow & \color{red}{23}x
& = &22\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{22}{23} \\\Leftrightarrow & \color{green}{ x = \frac{22}{23} } & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+12}& = & -7 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{+12}\color{blue}{-12-14x }
& = & -7 \color{red}{ +14x }\color{blue}{-12-14x } \\\Leftrightarrow & 9x \color{blue}{-14x }
& = & -7 \color{blue}{-12} \\\Leftrightarrow &-5x
& = &-19\\\Leftrightarrow & \color{red}{-5}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-12}& = & 11 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12-8x }
& = & 11 \color{red}{ +8x }\color{blue}{+12-8x } \\\Leftrightarrow & 7x \color{blue}{-8x }
& = & 11 \color{blue}{+12} \\\Leftrightarrow &-x
& = &23\\\Leftrightarrow & \color{red}{-}x
& = &23\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{23}{-1} \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+14}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-x }
& = & -12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -12 \color{blue}{-14} \\\Leftrightarrow &-8x
& = &-26\\\Leftrightarrow & \color{red}{-8}x
& = &-26\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-26}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+11}& = & -10 \color{red}{ +13x } \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11-13x }
& = & -10 \color{red}{ +13x }\color{blue}{-11-13x } \\\Leftrightarrow & -6x \color{blue}{-13x }
& = & -10 \color{blue}{-11} \\\Leftrightarrow &-19x
& = &-21\\\Leftrightarrow & \color{red}{-19}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{-21}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{21}{19} } & & \\ & V = \left\{ \frac{21}{19} \right\} & \\\end{align}\)