Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(12x+9=6-11x\)
- \(x-5=13+3x\)
- \(-6x-1=-12+x\)
- \(5x+2=-15+11x\)
- \(15x+1=5-11x\)
- \(11x+9=2-10x\)
- \(-9x-14=2+x\)
- \(3x+3=2+13x\)
- \(-x+6=13+9x\)
- \(-10x-6=9+x\)
- \(4x-12=-10+5x\)
- \(-x-14=-3-11x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 12x \color{red}{+9}& = & 6 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9+11x }
& = & 6 \color{red}{ -11x }\color{blue}{-9+11x } \\\Leftrightarrow & 12x \color{blue}{+11x }
& = & 6 \color{blue}{-9} \\\Leftrightarrow &23x
& = &-3\\\Leftrightarrow & \color{red}{23}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-5}& = & 13 \color{red}{ +3x } \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5-3x }
& = & 13 \color{red}{ +3x }\color{blue}{+5-3x } \\\Leftrightarrow & x \color{blue}{-3x }
& = & 13 \color{blue}{+5} \\\Leftrightarrow &-2x
& = &18\\\Leftrightarrow & \color{red}{-2}x
& = &18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}}
& = & \frac{18}{-2} \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-1}\color{blue}{+1-x }
& = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & -12 \color{blue}{+1} \\\Leftrightarrow &-7x
& = &-11\\\Leftrightarrow & \color{red}{-7}x
& = &-11\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-11}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+2}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-11x }
& = & -15 \color{red}{ +11x }\color{blue}{-2-11x } \\\Leftrightarrow & 5x \color{blue}{-11x }
& = & -15 \color{blue}{-2} \\\Leftrightarrow &-6x
& = &-17\\\Leftrightarrow & \color{red}{-6}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{-17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{17}{6} } & & \\ & V = \left\{ \frac{17}{6} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+1}& = & 5 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1+11x }
& = & 5 \color{red}{ -11x }\color{blue}{-1+11x } \\\Leftrightarrow & 15x \color{blue}{+11x }
& = & 5 \color{blue}{-1} \\\Leftrightarrow &26x
& = &4\\\Leftrightarrow & \color{red}{26}x
& = &4\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}}
& = & \frac{4}{26} \\\Leftrightarrow & \color{green}{ x = \frac{2}{13} } & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+9}& = & 2 \color{red}{ -10x } \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9+10x }
& = & 2 \color{red}{ -10x }\color{blue}{-9+10x } \\\Leftrightarrow & 11x \color{blue}{+10x }
& = & 2 \color{blue}{-9} \\\Leftrightarrow &21x
& = &-7\\\Leftrightarrow & \color{red}{21}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{21}x}{ \color{blue}{ 21}}
& = & \frac{-7}{21} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-14}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-14}\color{blue}{+14-x }
& = & 2 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 2 \color{blue}{+14} \\\Leftrightarrow &-10x
& = &16\\\Leftrightarrow & \color{red}{-10}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{+3}& = & 2 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3-13x }
& = & 2 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 3x \color{blue}{-13x }
& = & 2 \color{blue}{-3} \\\Leftrightarrow &-10x
& = &-1\\\Leftrightarrow & \color{red}{-10}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{10} } & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+6}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6-9x }
& = & 13 \color{red}{ +9x }\color{blue}{-6-9x } \\\Leftrightarrow & -x \color{blue}{-9x }
& = & 13 \color{blue}{-6} \\\Leftrightarrow &-10x
& = &7\\\Leftrightarrow & \color{red}{-10}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-6}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-6}\color{blue}{+6-x }
& = & 9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & 9 \color{blue}{+6} \\\Leftrightarrow &-11x
& = &15\\\Leftrightarrow & \color{red}{-11}x
& = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 4x \color{red}{-12}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-5x }
& = & -10 \color{red}{ +5x }\color{blue}{+12-5x } \\\Leftrightarrow & 4x \color{blue}{-5x }
& = & -10 \color{blue}{+12} \\\Leftrightarrow &-x
& = &2\\\Leftrightarrow & \color{red}{-}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}}
& = & \frac{2}{-1} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{-14}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+11x }
& = & -3 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & -x \color{blue}{+11x }
& = & -3 \color{blue}{+14} \\\Leftrightarrow &10x
& = &11\\\Leftrightarrow & \color{red}{10}x
& = &11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)