Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(14x-7=-7+9x\)
- \(-8x+4=-14+9x\)
- \(-12x+2=3+x\)
- \(-5x-13=13+x\)
- \(-4x+2=-10+x\)
- \(12x-2=-5+11x\)
- \(-9x+15=1+7x\)
- \(x-11=-4-11x\)
- \(5x+1=-4-7x\)
- \(11x-15=-3-8x\)
- \(-12x-2=-3+x\)
- \(-12x-6=10+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 14x \color{red}{-7}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7-9x }
& = & -7 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 14x \color{blue}{-9x }
& = & -7 \color{blue}{+7} \\\Leftrightarrow &5x
& = &0\\\Leftrightarrow & \color{red}{5}x
& = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{+4}& = & -14 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-9x }
& = & -14 \color{red}{ +9x }\color{blue}{-4-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & -14 \color{blue}{-4} \\\Leftrightarrow &-17x
& = &-18\\\Leftrightarrow & \color{red}{-17}x
& = &-18\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{-18}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{18}{17} } & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{+2}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x }
& = & 3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 3 \color{blue}{-2} \\\Leftrightarrow &-13x
& = &1\\\Leftrightarrow & \color{red}{-13}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{-13}& = & 13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-13}\color{blue}{+13-x }
& = & 13 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 13 \color{blue}{+13} \\\Leftrightarrow &-6x
& = &26\\\Leftrightarrow & \color{red}{-6}x
& = &26\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{26}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2-x }
& = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -10 \color{blue}{-2} \\\Leftrightarrow &-5x
& = &-12\\\Leftrightarrow & \color{red}{-5}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{-12}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
- \(\begin{align} & 12x \color{red}{-2}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-11x }
& = & -5 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & 12x \color{blue}{-11x }
& = & -5 \color{blue}{+2} \\\Leftrightarrow &x
& = &-3\\\Leftrightarrow & \color{red}{}x
& = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
- \(\begin{align} & -9x \color{red}{+15}& = & 1 \color{red}{ +7x } \\\Leftrightarrow & -9x \color{red}{+15}\color{blue}{-15-7x }
& = & 1 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -9x \color{blue}{-7x }
& = & 1 \color{blue}{-15} \\\Leftrightarrow &-16x
& = &-14\\\Leftrightarrow & \color{red}{-16}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}}
& = & \frac{-14}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
- \(\begin{align} & x \color{red}{-11}& = & -4 \color{red}{ -11x } \\\Leftrightarrow & x \color{red}{-11}\color{blue}{+11+11x }
& = & -4 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & x \color{blue}{+11x }
& = & -4 \color{blue}{+11} \\\Leftrightarrow &12x
& = &7\\\Leftrightarrow & \color{red}{12}x
& = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 5x \color{red}{+1}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1+7x }
& = & -4 \color{red}{ -7x }\color{blue}{-1+7x } \\\Leftrightarrow & 5x \color{blue}{+7x }
& = & -4 \color{blue}{-1} \\\Leftrightarrow &12x
& = &-5\\\Leftrightarrow & \color{red}{12}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}}
& = & \frac{-5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-15}& = & -3 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15+8x }
& = & -3 \color{red}{ -8x }\color{blue}{+15+8x } \\\Leftrightarrow & 11x \color{blue}{+8x }
& = & -3 \color{blue}{+15} \\\Leftrightarrow &19x
& = &12\\\Leftrightarrow & \color{red}{19}x
& = &12\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{12}{19} \\\Leftrightarrow & \color{green}{ x = \frac{12}{19} } & & \\ & V = \left\{ \frac{12}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2-x }
& = & -3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & -3 \color{blue}{+2} \\\Leftrightarrow &-13x
& = &-1\\\Leftrightarrow & \color{red}{-13}x
& = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -12x \color{red}{-6}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x }
& = & 10 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x }
& = & 10 \color{blue}{+6} \\\Leftrightarrow &-13x
& = &16\\\Leftrightarrow & \color{red}{-13}x
& = &16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}}
& = & \frac{16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)