Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x+6=-9+x\)
- \(-10x-3=-11+x\)
- \(14x+3=15+3x\)
- \(-8x-10=10+x\)
- \(3x-12=-5-5x\)
- \(-14x+11=1+x\)
- \(10x-4=-10+9x\)
- \(15x+10=8-14x\)
- \(-11x+9=9+x\)
- \(-7x-1=-13+x\)
- \(14x+2=-10+x\)
- \(6x+7=8+x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-x }
& = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & -9 \color{blue}{-6} \\\Leftrightarrow &-10x
& = &-15\\\Leftrightarrow & \color{red}{-10}x
& = &-15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{-15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{-3}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3-x }
& = & -11 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -10x \color{blue}{-x }
& = & -11 \color{blue}{+3} \\\Leftrightarrow &-11x
& = &-8\\\Leftrightarrow & \color{red}{-11}x
& = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}}
& = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+3}& = & 15 \color{red}{ +3x } \\\Leftrightarrow & 14x \color{red}{+3}\color{blue}{-3-3x }
& = & 15 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 14x \color{blue}{-3x }
& = & 15 \color{blue}{-3} \\\Leftrightarrow &11x
& = &12\\\Leftrightarrow & \color{red}{11}x
& = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-10}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-10}\color{blue}{+10-x }
& = & 10 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -8x \color{blue}{-x }
& = & 10 \color{blue}{+10} \\\Leftrightarrow &-9x
& = &20\\\Leftrightarrow & \color{red}{-9}x
& = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-12}& = & -5 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12+5x }
& = & -5 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 3x \color{blue}{+5x }
& = & -5 \color{blue}{+12} \\\Leftrightarrow &8x
& = &7\\\Leftrightarrow & \color{red}{8}x
& = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+11}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11-x }
& = & 1 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & 1 \color{blue}{-11} \\\Leftrightarrow &-15x
& = &-10\\\Leftrightarrow & \color{red}{-15}x
& = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-4}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4-9x }
& = & -10 \color{red}{ +9x }\color{blue}{+4-9x } \\\Leftrightarrow & 10x \color{blue}{-9x }
& = & -10 \color{blue}{+4} \\\Leftrightarrow &x
& = &-6\\\Leftrightarrow & \color{red}{}x
& = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}}
& = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
- \(\begin{align} & 15x \color{red}{+10}& = & 8 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10+14x }
& = & 8 \color{red}{ -14x }\color{blue}{-10+14x } \\\Leftrightarrow & 15x \color{blue}{+14x }
& = & 8 \color{blue}{-10} \\\Leftrightarrow &29x
& = &-2\\\Leftrightarrow & \color{red}{29}x
& = &-2\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}}
& = & \frac{-2}{29} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{29} } & & \\ & V = \left\{ \frac{-2}{29} \right\} & \\\end{align}\)
- \(\begin{align} & -11x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9-x }
& = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -11x \color{blue}{-x }
& = & 9 \color{blue}{-9} \\\Leftrightarrow &-12x
& = &0\\\Leftrightarrow & \color{red}{-12}x
& = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{-1}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-1}\color{blue}{+1-x }
& = & -13 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -13 \color{blue}{+1} \\\Leftrightarrow &-8x
& = &-12\\\Leftrightarrow & \color{red}{-8}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
- \(\begin{align} & 14x \color{red}{+2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2-x }
& = & -10 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & 14x \color{blue}{-x }
& = & -10 \color{blue}{-2} \\\Leftrightarrow &13x
& = &-12\\\Leftrightarrow & \color{red}{13}x
& = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
- \(\begin{align} & 6x \color{red}{+7}& = & 8 \color{red}{ +x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7-x }
& = & 8 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 6x \color{blue}{-x }
& = & 8 \color{blue}{-7} \\\Leftrightarrow &5x
& = &1\\\Leftrightarrow & \color{red}{5}x
& = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}}
& = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)