Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
- \(-9x-11=2+x\)
- \(-4x-11=-8+x\)
- \(-x+4=-1+11x\)
- \(10x-6=11-9x\)
- \(7x+1=-6+10x\)
- \(9x-3=15+x\)
- \(-5x+7=10+x\)
- \(-8x-5=8+9x\)
- \(7x+7=-14-13x\)
- \(-3x+6=-1+4x\)
- \(9x+13=-7-13x\)
- \(-5x+1=12+13x\)
Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk
Verbetersleutel
- \(\begin{align} & -9x \color{red}{-11}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11-x }
& = & 2 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -9x \color{blue}{-x }
& = & 2 \color{blue}{+11} \\\Leftrightarrow &-10x
& = &13\\\Leftrightarrow & \color{red}{-10}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}}
& = & \frac{13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
- \(\begin{align} & -4x \color{red}{-11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-11}\color{blue}{+11-x }
& = & -8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -4x \color{blue}{-x }
& = & -8 \color{blue}{+11} \\\Leftrightarrow &-5x
& = &3\\\Leftrightarrow & \color{red}{-5}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}}
& = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
- \(\begin{align} & -x \color{red}{+4}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4-11x }
& = & -1 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -x \color{blue}{-11x }
& = & -1 \color{blue}{-4} \\\Leftrightarrow &-12x
& = &-5\\\Leftrightarrow & \color{red}{-12}x
& = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}}
& = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
- \(\begin{align} & 10x \color{red}{-6}& = & 11 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6+9x }
& = & 11 \color{red}{ -9x }\color{blue}{+6+9x } \\\Leftrightarrow & 10x \color{blue}{+9x }
& = & 11 \color{blue}{+6} \\\Leftrightarrow &19x
& = &17\\\Leftrightarrow & \color{red}{19}x
& = &17\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}}
& = & \frac{17}{19} \\\Leftrightarrow & \color{green}{ x = \frac{17}{19} } & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+1}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{+1}\color{blue}{-1-10x }
& = & -6 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & 7x \color{blue}{-10x }
& = & -6 \color{blue}{-1} \\\Leftrightarrow &-3x
& = &-7\\\Leftrightarrow & \color{red}{-3}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}}
& = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{-3}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-3}\color{blue}{+3-x }
& = & 15 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & 9x \color{blue}{-x }
& = & 15 \color{blue}{+3} \\\Leftrightarrow &8x
& = &18\\\Leftrightarrow & \color{red}{8}x
& = &18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}}
& = & \frac{18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7-x }
& = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -5x \color{blue}{-x }
& = & 10 \color{blue}{-7} \\\Leftrightarrow &-6x
& = &3\\\Leftrightarrow & \color{red}{-6}x
& = &3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}}
& = & \frac{3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
- \(\begin{align} & -8x \color{red}{-5}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-9x }
& = & 8 \color{red}{ +9x }\color{blue}{+5-9x } \\\Leftrightarrow & -8x \color{blue}{-9x }
& = & 8 \color{blue}{+5} \\\Leftrightarrow &-17x
& = &13\\\Leftrightarrow & \color{red}{-17}x
& = &13\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}}
& = & \frac{13}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
- \(\begin{align} & 7x \color{red}{+7}& = & -14 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7+13x }
& = & -14 \color{red}{ -13x }\color{blue}{-7+13x } \\\Leftrightarrow & 7x \color{blue}{+13x }
& = & -14 \color{blue}{-7} \\\Leftrightarrow &20x
& = &-21\\\Leftrightarrow & \color{red}{20}x
& = &-21\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}}
& = & \frac{-21}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{20} } & & \\ & V = \left\{ \frac{-21}{20} \right\} & \\\end{align}\)
- \(\begin{align} & -3x \color{red}{+6}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6-4x }
& = & -1 \color{red}{ +4x }\color{blue}{-6-4x } \\\Leftrightarrow & -3x \color{blue}{-4x }
& = & -1 \color{blue}{-6} \\\Leftrightarrow &-7x
& = &-7\\\Leftrightarrow & \color{red}{-7}x
& = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}}
& = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
- \(\begin{align} & 9x \color{red}{+13}& = & -7 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13+13x }
& = & -7 \color{red}{ -13x }\color{blue}{-13+13x } \\\Leftrightarrow & 9x \color{blue}{+13x }
& = & -7 \color{blue}{-13} \\\Leftrightarrow &22x
& = &-20\\\Leftrightarrow & \color{red}{22}x
& = &-20\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}}
& = & \frac{-20}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)
- \(\begin{align} & -5x \color{red}{+1}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1-13x }
& = & 12 \color{red}{ +13x }\color{blue}{-1-13x } \\\Leftrightarrow & -5x \color{blue}{-13x }
& = & 12 \color{blue}{-1} \\\Leftrightarrow &-18x
& = &11\\\Leftrightarrow & \color{red}{-18}x
& = &11\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}}
& = & \frac{11}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{18} } & & \\ & V = \left\{ \frac{-11}{18} \right\} & \\\end{align}\)