Vgln. eerste graad (reeks 3)

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reeks met haakjes

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

reeks met haakjes

Verbetersleutel

  1. \(\begin{align} & \color{red}{3} (5x+5)& = & -15 \color{red}{+} (9+2x) \\\Leftrightarrow & 15x+15& = &-15+9+2x \\\Leftrightarrow & 15x \color{red}{+15} & = &-6 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &-6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 15x-2x& = &-6-15 \\\Leftrightarrow & 13x& = &-21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\\end{align}\)
  2. \(\begin{align} & \color{red}{4} (-4x+3)& = & 15 \color{red}{+} (-14+3x) \\\Leftrightarrow & -16x+12& = &15-14+3x \\\Leftrightarrow & -16x \color{red}{+12} & = &1 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -16x-3x& = &1-12 \\\Leftrightarrow & -19x& = &-11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\\end{align}\)
  3. \(\begin{align} & \color{red}{2} (-4x+7)& = & -9 \color{red}{-} (-12-5x) \\\Leftrightarrow & -8x+14& = &-9+12+5x \\\Leftrightarrow & -8x \color{red}{+14} & = &3 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-14} \\\Leftrightarrow & -8x-5x& = &3-14 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\\end{align}\)
  4. \(\begin{align} & \color{red}{3} (-x+3)& = & -11 \color{red}{-} (-13-5x) \\\Leftrightarrow & -3x+9& = &-11+13+5x \\\Leftrightarrow & -3x \color{red}{+9} & = &2 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & -3x-5x& = &2-9 \\\Leftrightarrow & -8x& = &-7 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-7}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{7}{8} & & \\\end{align}\)
  5. \(\begin{align} & \color{red}{2} (4x+3)& = & 2 \color{red}{-} (-15+3x) \\\Leftrightarrow & 8x+6& = &2+15-3x \\\Leftrightarrow & 8x \color{red}{+6} & = &17 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 8x+3x& = &17-6 \\\Leftrightarrow & 11x& = &11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{11}{ \color{red}{11} } \\\Leftrightarrow & x = 1 & & \\\end{align}\)
  6. \(\begin{align} & \color{red}{5} (4x+3)& = & 6 \color{red}{+} (14+3x) \\\Leftrightarrow & 20x+15& = &6+14+3x \\\Leftrightarrow & 20x \color{red}{+15} & = &20 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{-3x} & = &20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-15} \\\Leftrightarrow & 20x-3x& = &20-15 \\\Leftrightarrow & 17x& = &5 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{5}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{5}{17} & & \\\end{align}\)
  7. \(\begin{align} & \color{red}{3} (6x+5)& = & 6 \color{red}{+} (-7+5x) \\\Leftrightarrow & 18x+15& = &6-7+5x \\\Leftrightarrow & 18x \color{red}{+15} & = &-1 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-15} \\\Leftrightarrow & 18x-5x& = &-1-15 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\\end{align}\)
  8. \(\begin{align} & \color{red}{2} (-6x-7)& = & 5 \color{red}{+} (-2+5x) \\\Leftrightarrow & -12x-14& = &5-2+5x \\\Leftrightarrow & -12x \color{red}{-14} & = &3 \color{red}{+5x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+14} \\\Leftrightarrow & -12x-5x& = &3+14 \\\Leftrightarrow & -17x& = &17 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{17}{ \color{red}{-17} } \\\Leftrightarrow & x = -1 & & \\\end{align}\)
  9. \(\begin{align} & \color{red}{4} (-3x+4)& = & -1 \color{red}{+} (9+5x) \\\Leftrightarrow & -12x+16& = &-1+9+5x \\\Leftrightarrow & -12x \color{red}{+16} & = &8 \color{red}{+5x} \\\Leftrightarrow & -12x \color{red}{+16} \color{blue}{-16} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-16} \\\Leftrightarrow & -12x-5x& = &8-16 \\\Leftrightarrow & -17x& = &-8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{8}{17} & & \\\end{align}\)
  10. \(\begin{align} & \color{red}{2} (2x+2)& = & -8 \color{red}{-} (-8+x) \\\Leftrightarrow & 4x+4& = &-8+8-x \\\Leftrightarrow & 4x \color{red}{+4} & = &0 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 4x+x& = &0-4 \\\Leftrightarrow & 5x& = &-4 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-4}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-4}{5} & & \\\end{align}\)
  11. \(\begin{align} & \color{red}{6} (x-1)& = & -4 \color{red}{+} (-5+5x) \\\Leftrightarrow & 6x-6& = &-4-5+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &-9+6 \\\Leftrightarrow & x& = &-3 \\\end{align}\)
  12. \(\begin{align} & \color{red}{5} (3x+5)& = & -3 \color{red}{+} (-8-2x) \\\Leftrightarrow & 15x+25& = &-3-8-2x \\\Leftrightarrow & 15x \color{red}{+25} & = &-11 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+25} \color{blue}{-25} \color{blue}{+2x} & = &-11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-25} \\\Leftrightarrow & 15x+2x& = &-11-25 \\\Leftrightarrow & 17x& = &-36 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-36}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-36}{17} & & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 02:27:29