Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (3x+4)& = & -8 \color{red}{+} (-12+x) \\\Leftrightarrow & 15x+20& = &-8-12+x \\\Leftrightarrow & 15x \color{red}{+20} & = &-20 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 15x-x& = &-20-20 \\\Leftrightarrow & 14x& = &-40 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-40}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-2)& = & -6 \color{red}{-} (11-5x) \\\Leftrightarrow & 36x-12& = &-6-11+5x \\\Leftrightarrow & 36x \color{red}{-12} & = &-17 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-17 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 36x-5x& = &-17+12 \\\Leftrightarrow & 31x& = &-5 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-5}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-5}{31} & & \\ & V = \left\{ \frac{-5}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+6)& = & -3 \color{red}{+} (8+4x) \\\Leftrightarrow & 25x+30& = &-3+8+4x \\\Leftrightarrow & 25x \color{red}{+30} & = &5 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-30} \\\Leftrightarrow & 25x-4x& = &5-30 \\\Leftrightarrow & 21x& = &-25 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-25}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-25}{21} & & \\ & V = \left\{ \frac{-25}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-x+4)& = & -15 \color{red}{-} (-12+x) \\\Leftrightarrow & -4x+16& = &-15+12-x \\\Leftrightarrow & -4x \color{red}{+16} & = &-3 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -4x+x& = &-3-16 \\\Leftrightarrow & -3x& = &-19 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-19}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{19}{3} & & \\ & V = \left\{ \frac{19}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x+3)& = & -11 \color{red}{-} (15+x) \\\Leftrightarrow & 5x+15& = &-11-15-x \\\Leftrightarrow & 5x \color{red}{+15} & = &-26 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 5x+x& = &-26-15 \\\Leftrightarrow & 6x& = &-41 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-41}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-41}{6} & & \\ & V = \left\{ \frac{-41}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x-5)& = & 14 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-10& = &14-1+x \\\Leftrightarrow & 12x \color{red}{-10} & = &13 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 12x-x& = &13+10 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-5)& = & 6 \color{red}{-} (5+x) \\\Leftrightarrow & 30x-30& = &6-5-x \\\Leftrightarrow & 30x \color{red}{-30} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 30x+x& = &1+30 \\\Leftrightarrow & 31x& = &31 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{31}{ \color{red}{31} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-5x-4)& = & 1 \color{red}{+} (4+x) \\\Leftrightarrow & -30x-24& = &1+4+x \\\Leftrightarrow & -30x \color{red}{-24} & = &5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -30x-x& = &5+24 \\\Leftrightarrow & -31x& = &29 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{29}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-29}{31} & & \\ & V = \left\{ \frac{-29}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x-3)& = & 2 \color{red}{+} (10+x) \\\Leftrightarrow & -24x-18& = &2+10+x \\\Leftrightarrow & -24x \color{red}{-18} & = &12 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -24x-x& = &12+18 \\\Leftrightarrow & -25x& = &30 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{30}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x-1)& = & 11 \color{red}{+} (9+x) \\\Leftrightarrow & -12x-3& = &11+9+x \\\Leftrightarrow & -12x \color{red}{-3} & = &20 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &20+3 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x+3)& = & 13 \color{red}{+} (-12-5x) \\\Leftrightarrow & -36x+18& = &13-12-5x \\\Leftrightarrow & -36x \color{red}{+18} & = &1 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -36x+5x& = &1-18 \\\Leftrightarrow & -31x& = &-17 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-17}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{17}{31} & & \\ & V = \left\{ \frac{17}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-2x-6)& = & -3 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x-36& = &-3+15-x \\\Leftrightarrow & -12x \color{red}{-36} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -12x+x& = &12+36 \\\Leftrightarrow & -11x& = &48 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{48}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-48}{11} & & \\ & V = \left\{ \frac{-48}{11} \right\} & \\\end{align}\)