Vgln. eerste graad (reeks 2)

Hoofdmenu Eentje per keer 

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

  1. \(\begin{align} & 13x \color{red}{-3}& = & -7 \color{red}{ +9x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3-9x } & = & -7 \color{red}{ +9x }\color{blue}{+3-9x } \\\Leftrightarrow & 13x \color{blue}{-9x } & = & -7 \color{blue}{+3} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\\end{align}\)
  2. \(\begin{align} & -x \color{red}{+14}& = & 14 \color{red}{ +12x } \\\Leftrightarrow & -x \color{red}{+14}\color{blue}{-14-12x } & = & 14 \color{red}{ +12x }\color{blue}{-14-12x } \\\Leftrightarrow & -x \color{blue}{-12x } & = & 14 \color{blue}{-14} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\\end{align}\)
  3. \(\begin{align} & -15x \color{red}{-11}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11+7x } & = & -14 \color{red}{ -7x }\color{blue}{+11+7x } \\\Leftrightarrow & -15x \color{blue}{+7x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\\end{align}\)
  4. \(\begin{align} & -11x \color{red}{+1}& = & 13 \color{red}{ -8x } \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1+8x } & = & 13 \color{red}{ -8x }\color{blue}{-1+8x } \\\Leftrightarrow & -11x \color{blue}{+8x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\\end{align}\)
  5. \(\begin{align} & 11x \color{red}{+2}& = & 10 \color{red}{ +6x } \\\Leftrightarrow & 11x \color{red}{+2}\color{blue}{-2-6x } & = & 10 \color{red}{ +6x }\color{blue}{-2-6x } \\\Leftrightarrow & 11x \color{blue}{-6x } & = & 10 \color{blue}{-2} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\\end{align}\)
  6. \(\begin{align} & -7x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-x } & = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-8x & = &30\\\Leftrightarrow & \color{red}{-8}x & = &30\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{30}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\\end{align}\)
  7. \(\begin{align} & 12x \color{red}{+11}& = & 8 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11+11x } & = & 8 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\\end{align}\)
  8. \(\begin{align} & 8x \color{red}{-1}& = & -4 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{-1}\color{blue}{+1-3x } & = & -4 \color{red}{ +3x }\color{blue}{+1-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\\end{align}\)
  9. \(\begin{align} & -3x \color{red}{+6}& = & 15 \color{red}{ -8x } \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6+8x } & = & 15 \color{red}{ -8x }\color{blue}{-6+8x } \\\Leftrightarrow & -3x \color{blue}{+8x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\\end{align}\)
  10. \(\begin{align} & 12x \color{red}{+3}& = & -11 \color{red}{ +13x } \\\Leftrightarrow & 12x \color{red}{+3}\color{blue}{-3-13x } & = & -11 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & 12x \color{blue}{-13x } & = & -11 \color{blue}{-3} \\\Leftrightarrow &-x & = &-14\\\Leftrightarrow & \color{red}{-}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-14}{-1} \\\Leftrightarrow & \color{green}{ x = 14 } & & \\\end{align}\)
  11. \(\begin{align} & 5x \color{red}{-11}& = & -12 \color{red}{ +12x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11-12x } & = & -12 \color{red}{ +12x }\color{blue}{+11-12x } \\\Leftrightarrow & 5x \color{blue}{-12x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\\end{align}\)
  12. \(\begin{align} & -12x \color{red}{+8}& = & -13 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8-13x } & = & -13 \color{red}{ +13x }\color{blue}{-8-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-25x & = &-21\\\Leftrightarrow & \color{red}{-25}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-21}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{21}{25} } & & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 01:13:52