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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

  1. \(12x-11=7-11x\)
  2. \(-11x+12=-8+4x\)
  3. \(-4x-1=11+15x\)
  4. \(11x-4=-5+4x\)
  5. \(8x-14=-3-5x\)
  6. \(x-9=10-13x\)
  7. \(-7x+4=-15+11x\)
  8. \(13x-6=11+3x\)
  9. \(-3x+13=7-5x\)
  10. \(-10x+2=13+9x\)
  11. \(-9x-5=-4-2x\)
  12. \(10x-5=7+x\)

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

  1. \(\begin{align} & 12x \color{red}{-11}& = & 7 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11+11x } & = & 7 \color{red}{ -11x }\color{blue}{+11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 7 \color{blue}{+11} \\\Leftrightarrow &23x & = &18\\\Leftrightarrow & \color{red}{23}x & = &18\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{18}{23} \\\Leftrightarrow & \color{green}{ x = \frac{18}{23} } & & \\\end{align}\)
  2. \(\begin{align} & -11x \color{red}{+12}& = & -8 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-4x } & = & -8 \color{red}{ +4x }\color{blue}{-12-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & -8 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\\end{align}\)
  3. \(\begin{align} & -4x \color{red}{-1}& = & 11 \color{red}{ +15x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-15x } & = & 11 \color{red}{ +15x }\color{blue}{+1-15x } \\\Leftrightarrow & -4x \color{blue}{-15x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-19x & = &12\\\Leftrightarrow & \color{red}{-19}x & = &12\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{12}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{19} } & & \\\end{align}\)
  4. \(\begin{align} & 11x \color{red}{-4}& = & -5 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4-4x } & = & -5 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & -5 \color{blue}{+4} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\\end{align}\)
  5. \(\begin{align} & 8x \color{red}{-14}& = & -3 \color{red}{ -5x } \\\Leftrightarrow & 8x \color{red}{-14}\color{blue}{+14+5x } & = & -3 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 8x \color{blue}{+5x } & = & -3 \color{blue}{+14} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\\end{align}\)
  6. \(\begin{align} & x \color{red}{-9}& = & 10 \color{red}{ -13x } \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9+13x } & = & 10 \color{red}{ -13x }\color{blue}{+9+13x } \\\Leftrightarrow & x \color{blue}{+13x } & = & 10 \color{blue}{+9} \\\Leftrightarrow &14x & = &19\\\Leftrightarrow & \color{red}{14}x & = &19\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{19}{14} \\\Leftrightarrow & \color{green}{ x = \frac{19}{14} } & & \\\end{align}\)
  7. \(\begin{align} & -7x \color{red}{+4}& = & -15 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4-11x } & = & -15 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -15 \color{blue}{-4} \\\Leftrightarrow &-18x & = &-19\\\Leftrightarrow & \color{red}{-18}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-19}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{19}{18} } & & \\\end{align}\)
  8. \(\begin{align} & 13x \color{red}{-6}& = & 11 \color{red}{ +3x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-3x } & = & 11 \color{red}{ +3x }\color{blue}{+6-3x } \\\Leftrightarrow & 13x \color{blue}{-3x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &10x & = &17\\\Leftrightarrow & \color{red}{10}x & = &17\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{17}{10} \\\Leftrightarrow & \color{green}{ x = \frac{17}{10} } & & \\\end{align}\)
  9. \(\begin{align} & -3x \color{red}{+13}& = & 7 \color{red}{ -5x } \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13+5x } & = & 7 \color{red}{ -5x }\color{blue}{-13+5x } \\\Leftrightarrow & -3x \color{blue}{+5x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &2x & = &-6\\\Leftrightarrow & \color{red}{2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-6}{2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\\end{align}\)
  10. \(\begin{align} & -10x \color{red}{+2}& = & 13 \color{red}{ +9x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2-9x } & = & 13 \color{red}{ +9x }\color{blue}{-2-9x } \\\Leftrightarrow & -10x \color{blue}{-9x } & = & 13 \color{blue}{-2} \\\Leftrightarrow &-19x & = &11\\\Leftrightarrow & \color{red}{-19}x & = &11\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{11}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{19} } & & \\\end{align}\)
  11. \(\begin{align} & -9x \color{red}{-5}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5+2x } & = & -4 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & -9x \color{blue}{+2x } & = & -4 \color{blue}{+5} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\\end{align}\)
  12. \(\begin{align} & 10x \color{red}{-5}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5-x } & = & 7 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 7 \color{blue}{+5} \\\Leftrightarrow &9x & = &12\\\Leftrightarrow & \color{red}{9}x & = &12\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{12}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 07:06:28