Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (2x-6)& = & 3 \color{red}{+} (-7+x) \\\Leftrightarrow & 6x-18& = &3-7+x \\\Leftrightarrow & 6x \color{red}{-18} & = &-4 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 6x-x& = &-4+18 \\\Leftrightarrow & 5x& = &14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-7)& = & -13 \color{red}{-} (-4-5x) \\\Leftrightarrow & 18x-21& = &-13+4+5x \\\Leftrightarrow & 18x \color{red}{-21} & = &-9 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &-9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & 18x-5x& = &-9+21 \\\Leftrightarrow & 13x& = &12 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{12}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-5x+2)& = & 8 \color{red}{+} (-6+x) \\\Leftrightarrow & -15x+6& = &8-6+x \\\Leftrightarrow & -15x \color{red}{+6} & = &2 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -15x-x& = &2-6 \\\Leftrightarrow & -16x& = &-4 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{-4}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x+1)& = & -12 \color{red}{+} (-9+x) \\\Leftrightarrow & 24x+6& = &-12-9+x \\\Leftrightarrow & 24x \color{red}{+6} & = &-21 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-21 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 24x-x& = &-21-6 \\\Leftrightarrow & 23x& = &-27 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-27}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-27}{23} & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x+6)& = & -14 \color{red}{+} (-14+2x) \\\Leftrightarrow & 3x+18& = &-14-14+2x \\\Leftrightarrow & 3x \color{red}{+18} & = &-28 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &-28 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & 3x-2x& = &-28-18 \\\Leftrightarrow & x& = &-46 \\ & V = \left\{ -46 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (2x+1)& = & -4 \color{red}{-} (3-3x) \\\Leftrightarrow & 4x+2& = &-4-3+3x \\\Leftrightarrow & 4x \color{red}{+2} & = &-7 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & 4x-3x& = &-7-2 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x-6)& = & 2 \color{red}{-} (-15+2x) \\\Leftrightarrow & -15x-18& = &2+15-2x \\\Leftrightarrow & -15x \color{red}{-18} & = &17 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & -15x+2x& = &17+18 \\\Leftrightarrow & -13x& = &35 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{35}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-35}{13} & & \\ & V = \left\{ \frac{-35}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x-4)& = & -11 \color{red}{+} (15+x) \\\Leftrightarrow & 4x-8& = &-11+15+x \\\Leftrightarrow & 4x \color{red}{-8} & = &4 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 4x-x& = &4+8 \\\Leftrightarrow & 3x& = &12 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{12}{ \color{red}{3} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x+7)& = & -1 \color{red}{+} (-5+x) \\\Leftrightarrow & -3x+21& = &-1-5+x \\\Leftrightarrow & -3x \color{red}{+21} & = &-6 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -3x-x& = &-6-21 \\\Leftrightarrow & -4x& = &-27 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-27}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{27}{4} & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-7)& = & -12 \color{red}{-} (-9-3x) \\\Leftrightarrow & -4x-28& = &-12+9+3x \\\Leftrightarrow & -4x \color{red}{-28} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -4x-3x& = &-3+28 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x+5)& = & 8 \color{red}{+} (-1+x) \\\Leftrightarrow & -30x+30& = &8-1+x \\\Leftrightarrow & -30x \color{red}{+30} & = &7 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -30x-x& = &7-30 \\\Leftrightarrow & -31x& = &-23 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-23}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{23}{31} & & \\ & V = \left\{ \frac{23}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x-7)& = & -15 \color{red}{+} (6+x) \\\Leftrightarrow & 12x-14& = &-15+6+x \\\Leftrightarrow & 12x \color{red}{-14} & = &-9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &-9+14 \\\Leftrightarrow & 11x& = &5 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{5}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)