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