Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(6x+6=7+x\)
- \(-10x+4=-6+x\)
- \(-13x-9=-11+x\)
- \(15x-12=-15-7x\)
- \(15x+7=5-2x\)
- \(9x-8=2-11x\)
- \(10x+8=6+x\)
- \(6x-3=-11+x\)
- \(-9x+1=9+x\)
- \(-3x-6=13+x\)
- \(2x+10=1+x\)
- \(-10x+13=-15+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 6x \color{red}{+6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+6}\color{blue}{-6-x }
& = & 7 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 7 \color{blue}{-6} \\\Leftrightarrow &5x
& = &1\\\Leftrightarrow & \color{red}{5}x
& = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-x }
& = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -6 \color{blue}{-4} \\\Leftrightarrow &-11x
& = &-10\\\Leftrightarrow & \color{red}{-11}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -13x \color{red}{-9}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x }
& = & -11 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x }
& = & -11 \color{blue}{+9} \\\Leftrightarrow &-14x
& = &-2\\\Leftrightarrow & \color{red}{-14}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}}
& = & \frac{-2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{-12}& = & -15 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+7x }
& = & -15 \color{red}{ -7x }\color{blue}{+12+7x } \\\Leftrightarrow & 15x \color{blue}{+7x }
& = & -15 \color{blue}{+12} \\\Leftrightarrow &22x
& = &-3\\\Leftrightarrow & \color{red}{22}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{-3}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{22} } & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+7}& = & 5 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+2x }
& = & 5 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 15x \color{blue}{+2x }
& = & 5 \color{blue}{-7} \\\Leftrightarrow &17x
& = &-2\\\Leftrightarrow & \color{red}{17}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}}
& = & \frac{-2}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{17} } & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-8}& = & 2 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8+11x }
& = & 2 \color{red}{ -11x }\color{blue}{+8+11x } \\\Leftrightarrow & 9x \color{blue}{+11x }
& = & 2 \color{blue}{+8} \\\Leftrightarrow &20x
& = &10\\\Leftrightarrow & \color{red}{20}x
& = &10\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{10}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{+8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8-x }
& = & 6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 10x \color{blue}{-x }
& = & 6 \color{blue}{-8} \\\Leftrightarrow &9x
& = &-2\\\Leftrightarrow & \color{red}{9}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}}
& = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3-x }
& = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & -11 \color{blue}{+3} \\\Leftrightarrow &5x
& = &-8\\\Leftrightarrow & \color{red}{5}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{-8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+1}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+1}\color{blue}{-1-x }
& = & 9 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 9 \color{blue}{-1} \\\Leftrightarrow &-10x
& = &8\\\Leftrightarrow & \color{red}{-10}x
& = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{-6}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x }
& = & 13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x }
& = & 13 \color{blue}{+6} \\\Leftrightarrow &-4x
& = &19\\\Leftrightarrow & \color{red}{-4}x
& = &19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}}
& = & \frac{19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{4} } & & \\ & V = \left\{ \frac{-19}{4} \right\} & \\\end{align}\)
- \(\begin{align} & 2x \color{red}{+10}& = & 1 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+10}\color{blue}{-10-x }
& = & 1 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 2x \color{blue}{-x }
& = & 1 \color{blue}{-10} \\\Leftrightarrow &x
& = &-9\\\Leftrightarrow & \color{red}{}x
& = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13-x }
& = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -15 \color{blue}{-13} \\\Leftrightarrow &-11x
& = &-28\\\Leftrightarrow & \color{red}{-11}x
& = &-28\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-28}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{28}{11} } & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)