Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x-7)& = & -9 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x-14& = &-9-9+x \\\Leftrightarrow & 12x \color{red}{-14} & = &-18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & 12x-x& = &-18+14 \\\Leftrightarrow & 11x& = &-4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x-4)& = & 3 \color{red}{+} (2-5x) \\\Leftrightarrow & 6x-24& = &3+2-5x \\\Leftrightarrow & 6x \color{red}{-24} & = &5 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 6x+5x& = &5+24 \\\Leftrightarrow & 11x& = &29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x+7)& = & -2 \color{red}{+} (-9+x) \\\Leftrightarrow & -2x+14& = &-2-9+x \\\Leftrightarrow & -2x \color{red}{+14} & = &-11 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -2x-x& = &-11-14 \\\Leftrightarrow & -3x& = &-25 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-25}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{25}{3} & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (3x+5)& = & 9 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x+20& = &9+11-x \\\Leftrightarrow & 12x \color{red}{+20} & = &20 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 12x+x& = &20-20 \\\Leftrightarrow & 13x& = &0 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{0}{ \color{red}{13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x-6)& = & 3 \color{red}{-} (-7-5x) \\\Leftrightarrow & -6x-36& = &3+7+5x \\\Leftrightarrow & -6x \color{red}{-36} & = &10 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-36} \color{blue}{+36} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+36} \\\Leftrightarrow & -6x-5x& = &10+36 \\\Leftrightarrow & -11x& = &46 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{46}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-46}{11} & & \\ & V = \left\{ \frac{-46}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (4x+7)& = & -4 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x+21& = &-4+11-x \\\Leftrightarrow & 12x \color{red}{+21} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 12x+x& = &7-21 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x-6)& = & 8 \color{red}{-} (2+x) \\\Leftrightarrow & -6x-12& = &8-2-x \\\Leftrightarrow & -6x \color{red}{-12} & = &6 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &6+12 \\\Leftrightarrow & -5x& = &18 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{18}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-18}{5} & & \\ & V = \left\{ \frac{-18}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x-1)& = & -15 \color{red}{+} (15+x) \\\Leftrightarrow & -6x-3& = &-15+15+x \\\Leftrightarrow & -6x \color{red}{-3} & = &0 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -6x-x& = &0+3 \\\Leftrightarrow & -7x& = &3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (3x-1)& = & -2 \color{red}{+} (6+x) \\\Leftrightarrow & 6x-2& = &-2+6+x \\\Leftrightarrow & 6x \color{red}{-2} & = &4 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & 6x-x& = &4+2 \\\Leftrightarrow & 5x& = &6 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{6}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x+4)& = & 5 \color{red}{+} (3+x) \\\Leftrightarrow & -12x+24& = &5+3+x \\\Leftrightarrow & -12x \color{red}{+24} & = &8 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -12x-x& = &8-24 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x-5)& = & -6 \color{red}{+} (4-5x) \\\Leftrightarrow & 18x-15& = &-6+4-5x \\\Leftrightarrow & 18x \color{red}{-15} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 18x+5x& = &-2+15 \\\Leftrightarrow & 23x& = &13 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{13}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{13}{23} & & \\ & V = \left\{ \frac{13}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x-6)& = & 3 \color{red}{+} (2+x) \\\Leftrightarrow & 20x-24& = &3+2+x \\\Leftrightarrow & 20x \color{red}{-24} & = &5 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 20x-x& = &5+24 \\\Leftrightarrow & 19x& = &29 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{29}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{29}{19} & & \\ & V = \left\{ \frac{29}{19} \right\} & \\\end{align}\)