Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-2x+9=9+x\)
- \(-6x+2=6+x\)
- \(x-1=10+6x\)
- \(5x-13=1-2x\)
- \(11x+13=-14+x\)
- \(-x+13=-10-15x\)
- \(15x+11=-2-7x\)
- \(6x+2=-3+x\)
- \(-6x+1=8+x\)
- \(-14x-15=-13+x\)
- \(-9x-2=-1+x\)
- \(9x+10=-15+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -2x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+9}\color{blue}{-9-x }
& = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -2x \color{blue}{-x }
& = & 9 \color{blue}{-9} \\\Leftrightarrow &-3x
& = &0\\\Leftrightarrow & \color{red}{-3}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+2}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x }
& = & 6 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 6 \color{blue}{-2} \\\Leftrightarrow &-7x
& = &4\\\Leftrightarrow & \color{red}{-7}x
& = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-1}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1-6x }
& = & 10 \color{red}{ +6x }\color{blue}{+1-6x } \\\Leftrightarrow & x \color{blue}{-6x }
& = & 10 \color{blue}{+1} \\\Leftrightarrow &-5x
& = &11\\\Leftrightarrow & \color{red}{-5}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{11}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{-13}& = & 1 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+2x }
& = & 1 \color{red}{ -2x }\color{blue}{+13+2x } \\\Leftrightarrow & 5x \color{blue}{+2x }
& = & 1 \color{blue}{+13} \\\Leftrightarrow &7x
& = &14\\\Leftrightarrow & \color{red}{7}x
& = &14\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}}
& = & \frac{14}{7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+13}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-x }
& = & -14 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 11x \color{blue}{-x }
& = & -14 \color{blue}{-13} \\\Leftrightarrow &10x
& = &-27\\\Leftrightarrow & \color{red}{10}x
& = &-27\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}}
& = & \frac{-27}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{10} } & & \\ & V = \left\{ \frac{-27}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+13}& = & -10 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{+13}\color{blue}{-13+15x }
& = & -10 \color{red}{ -15x }\color{blue}{-13+15x } \\\Leftrightarrow & -x \color{blue}{+15x }
& = & -10 \color{blue}{-13} \\\Leftrightarrow &14x
& = &-23\\\Leftrightarrow & \color{red}{14}x
& = &-23\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}}
& = & \frac{-23}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{14} } & & \\ & V = \left\{ \frac{-23}{14} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+11}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11+7x }
& = & -2 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 15x \color{blue}{+7x }
& = & -2 \color{blue}{-11} \\\Leftrightarrow &22x
& = &-13\\\Leftrightarrow & \color{red}{22}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{-13}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{22} } & & \\ & V = \left\{ \frac{-13}{22} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+2}\color{blue}{-2-x }
& = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -3 \color{blue}{-2} \\\Leftrightarrow &5x
& = &-5\\\Leftrightarrow & \color{red}{5}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -6x \color{red}{+1}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x }
& = & 8 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x }
& = & 8 \color{blue}{-1} \\\Leftrightarrow &-7x
& = &7\\\Leftrightarrow & \color{red}{-7}x
& = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-15}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15-x }
& = & -13 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -13 \color{blue}{+15} \\\Leftrightarrow &-15x
& = &2\\\Leftrightarrow & \color{red}{-15}x
& = &2\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{2}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{-2}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2-x }
& = & -1 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -1 \color{blue}{+2} \\\Leftrightarrow &-10x
& = &1\\\Leftrightarrow & \color{red}{-10}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10-x }
& = & -15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 9x \color{blue}{-x }
& = & -15 \color{blue}{-10} \\\Leftrightarrow &8x
& = &-25\\\Leftrightarrow & \color{red}{8}x
& = &-25\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{-25}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{8} } & & \\ & V = \left\{ \frac{-25}{8} \right\} & \\\end{align}\)