Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (4x+4)& = & 14 \color{red}{-} (-5+x) \\\Leftrightarrow & 20x+20& = &14+5-x \\\Leftrightarrow & 20x \color{red}{+20} & = &19 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 20x+x& = &19-20 \\\Leftrightarrow & 21x& = &-1 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-1}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+4)& = & 5 \color{red}{+} (14+x) \\\Leftrightarrow & 6x+12& = &5+14+x \\\Leftrightarrow & 6x \color{red}{+12} & = &19 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &19-12 \\\Leftrightarrow & 5x& = &7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x+4)& = & 14 \color{red}{-} (13+x) \\\Leftrightarrow & -8x+16& = &14-13-x \\\Leftrightarrow & -8x \color{red}{+16} & = &1 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & -8x+x& = &1-16 \\\Leftrightarrow & -7x& = &-15 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-15}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{15}{7} & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x+6)& = & -10 \color{red}{-} (10+x) \\\Leftrightarrow & -12x+12& = &-10-10-x \\\Leftrightarrow & -12x \color{red}{+12} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -12x+x& = &-20-12 \\\Leftrightarrow & -11x& = &-32 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-32}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x+2)& = & -11 \color{red}{-} (-11-3x) \\\Leftrightarrow & 4x+4& = &-11+11+3x \\\Leftrightarrow & 4x \color{red}{+4} & = &0 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & 4x-3x& = &0-4 \\\Leftrightarrow & x& = &-4 \\ & V = \left\{ -4 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (2x+7)& = & -1 \color{red}{-} (14-5x) \\\Leftrightarrow & 6x+21& = &-1-14+5x \\\Leftrightarrow & 6x \color{red}{+21} & = &-15 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & 6x-5x& = &-15-21 \\\Leftrightarrow & x& = &-36 \\ & V = \left\{ -36 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x-3)& = & 6 \color{red}{-} (11-3x) \\\Leftrightarrow & -4x-6& = &6-11+3x \\\Leftrightarrow & -4x \color{red}{-6} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & -4x-3x& = &-5+6 \\\Leftrightarrow & -7x& = &1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-2)& = & 15 \color{red}{-} (14+x) \\\Leftrightarrow & 3x-6& = &15-14-x \\\Leftrightarrow & 3x \color{red}{-6} & = &1 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 3x+x& = &1+6 \\\Leftrightarrow & 4x& = &7 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{7}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{7}{4} & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x+3)& = & 10 \color{red}{+} (-2+x) \\\Leftrightarrow & 18x+18& = &10-2+x \\\Leftrightarrow & 18x \color{red}{+18} & = &8 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 18x-x& = &8-18 \\\Leftrightarrow & 17x& = &-10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-10}{17} & & \\ & V = \left\{ \frac{-10}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-5x+1)& = & -9 \color{red}{-} (5-3x) \\\Leftrightarrow & -10x+2& = &-9-5+3x \\\Leftrightarrow & -10x \color{red}{+2} & = &-14 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &-14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -10x-3x& = &-14-2 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (4x-1)& = & -5 \color{red}{-} (1+3x) \\\Leftrightarrow & 20x-5& = &-5-1-3x \\\Leftrightarrow & 20x \color{red}{-5} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 20x+3x& = &-6+5 \\\Leftrightarrow & 23x& = &-1 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-1}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-1}{23} & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+2)& = & -11 \color{red}{-} (-7+x) \\\Leftrightarrow & 30x+10& = &-11+7-x \\\Leftrightarrow & 30x \color{red}{+10} & = &-4 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 30x+x& = &-4-10 \\\Leftrightarrow & 31x& = &-14 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-14}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)