Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(6x+13=6-5x\)
- \(11x-6=-5-7x\)
- \(8x+12=-7-15x\)
- \(-14x+15=-15+x\)
- \(7x-14=6-6x\)
- \(-7x+15=-6+x\)
- \(-14x+7=-7+x\)
- \(-10x+4=-13+11x\)
- \(-14x-1=10+5x\)
- \(-4x+8=-5+5x\)
- \(11x+15=-6-8x\)
- \(3x-13=-12+10x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & 6x \color{red}{+13}& = & 6 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13+5x }
& = & 6 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & 6x \color{blue}{+5x }
& = & 6 \color{blue}{-13} \\\Leftrightarrow &11x
& = &-7\\\Leftrightarrow & \color{red}{11}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}}
& = & \frac{-7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{-6}& = & -5 \color{red}{ -7x } \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6+7x }
& = & -5 \color{red}{ -7x }\color{blue}{+6+7x } \\\Leftrightarrow & 11x \color{blue}{+7x }
& = & -5 \color{blue}{+6} \\\Leftrightarrow &18x
& = &1\\\Leftrightarrow & \color{red}{18}x
& = &1\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}}
& = & \frac{1}{18} \\\Leftrightarrow & \color{green}{ x = \frac{1}{18} } & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
- \(\begin{align} & 8x \color{red}{+12}& = & -7 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12+15x }
& = & -7 \color{red}{ -15x }\color{blue}{-12+15x } \\\Leftrightarrow & 8x \color{blue}{+15x }
& = & -7 \color{blue}{-12} \\\Leftrightarrow &23x
& = &-19\\\Leftrightarrow & \color{red}{23}x
& = &-19\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}}
& = & \frac{-19}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{23} } & & \\ & V = \left\{ \frac{-19}{23} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+15}\color{blue}{-15-x }
& = & -15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -15 \color{blue}{-15} \\\Leftrightarrow &-15x
& = &-30\\\Leftrightarrow & \color{red}{-15}x
& = &-30\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-30}{-15} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{-14}& = & 6 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14+6x }
& = & 6 \color{red}{ -6x }\color{blue}{+14+6x } \\\Leftrightarrow & 7x \color{blue}{+6x }
& = & 6 \color{blue}{+14} \\\Leftrightarrow &13x
& = &20\\\Leftrightarrow & \color{red}{13}x
& = &20\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}}
& = & \frac{20}{13} \\\Leftrightarrow & \color{green}{ x = \frac{20}{13} } & & \\ & V = \left\{ \frac{20}{13} \right\} & \\\end{align}\)
- \(\begin{align} & -7x \color{red}{+15}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x }
& = & -6 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x }
& = & -6 \color{blue}{-15} \\\Leftrightarrow &-8x
& = &-21\\\Leftrightarrow & \color{red}{-8}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}}
& = & \frac{-21}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{21}{8} } & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{+7}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+7}\color{blue}{-7-x }
& = & -7 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -14x \color{blue}{-x }
& = & -7 \color{blue}{-7} \\\Leftrightarrow &-15x
& = &-14\\\Leftrightarrow & \color{red}{-15}x
& = &-14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}}
& = & \frac{-14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{14}{15} } & & \\ & V = \left\{ \frac{14}{15} \right\} & \\\end{align}\)
- \(\begin{align} & -10x \color{red}{+4}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4-11x }
& = & -13 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -10x \color{blue}{-11x }
& = & -13 \color{blue}{-4} \\\Leftrightarrow &-21x
& = &-17\\\Leftrightarrow & \color{red}{-21}x
& = &-17\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}}
& = & \frac{-17}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{17}{21} } & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
- \(\begin{align} & -14x \color{red}{-1}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1-5x }
& = & 10 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -14x \color{blue}{-5x }
& = & 10 \color{blue}{+1} \\\Leftrightarrow &-19x
& = &11\\\Leftrightarrow & \color{red}{-19}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}}
& = & \frac{11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\ & V = \left\{ \frac{-11}{19} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{+8}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-5x }
& = & -5 \color{red}{ +5x }\color{blue}{-8-5x } \\\Leftrightarrow & -4x \color{blue}{-5x }
& = & -5 \color{blue}{-8} \\\Leftrightarrow &-9x
& = &-13\\\Leftrightarrow & \color{red}{-9}x
& = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}}
& = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
- \(\begin{align} & 11x \color{red}{+15}& = & -6 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+8x }
& = & -6 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 11x \color{blue}{+8x }
& = & -6 \color{blue}{-15} \\\Leftrightarrow &19x
& = &-21\\\Leftrightarrow & \color{red}{19}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{-21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{19} } & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 3x \color{red}{-13}& = & -12 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13-10x }
& = & -12 \color{red}{ +10x }\color{blue}{+13-10x } \\\Leftrightarrow & 3x \color{blue}{-10x }
& = & -12 \color{blue}{+13} \\\Leftrightarrow &-7x
& = &1\\\Leftrightarrow & \color{red}{-7}x
& = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)