Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-5)& = & -14 \color{red}{-} (-9+2x) \\\Leftrightarrow & 3x-15& = &-14+9-2x \\\Leftrightarrow & 3x \color{red}{-15} & = &-5 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{+2x} & = &-5 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+15} \\\Leftrightarrow & 3x+2x& = &-5+15 \\\Leftrightarrow & 5x& = &10 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{10}{ \color{red}{5} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (x+3)& = & 6 \color{red}{-} (1+x) \\\Leftrightarrow & 2x+6& = &6-1-x \\\Leftrightarrow & 2x \color{red}{+6} & = &5 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 2x+x& = &5-6 \\\Leftrightarrow & 3x& = &-1 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-1}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+4)& = & 13 \color{red}{+} (10+x) \\\Leftrightarrow & 18x+12& = &13+10+x \\\Leftrightarrow & 18x \color{red}{+12} & = &23 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 18x-x& = &23-12 \\\Leftrightarrow & 17x& = &11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x-3)& = & -14 \color{red}{-} (-15+x) \\\Leftrightarrow & 4x-6& = &-14+15-x \\\Leftrightarrow & 4x \color{red}{-6} & = &1 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 4x+x& = &1+6 \\\Leftrightarrow & 5x& = &7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x+1)& = & 15 \color{red}{+} (-9+x) \\\Leftrightarrow & 12x+2& = &15-9+x \\\Leftrightarrow & 12x \color{red}{+2} & = &6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 12x-x& = &6-2 \\\Leftrightarrow & 11x& = &4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x+7)& = & -15 \color{red}{-} (-11-3x) \\\Leftrightarrow & -4x+28& = &-15+11+3x \\\Leftrightarrow & -4x \color{red}{+28} & = &-4 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &-4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & -4x-3x& = &-4-28 \\\Leftrightarrow & -7x& = &-32 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-32}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{32}{7} & & \\ & V = \left\{ \frac{32}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-5x+1)& = & 6 \color{red}{+} (-6+x) \\\Leftrightarrow & -20x+4& = &6-6+x \\\Leftrightarrow & -20x \color{red}{+4} & = &0 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -20x-x& = &0-4 \\\Leftrightarrow & -21x& = &-4 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-4}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-2)& = & -11 \color{red}{+} (1-2x) \\\Leftrightarrow & -3x-6& = &-11+1-2x \\\Leftrightarrow & -3x \color{red}{-6} & = &-10 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{+2x} & = &-10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+6} \\\Leftrightarrow & -3x+2x& = &-10+6 \\\Leftrightarrow & -x& = &-4 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-4}{ \color{red}{-1} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x+2)& = & -3 \color{red}{+} (15-5x) \\\Leftrightarrow & -36x+12& = &-3+15-5x \\\Leftrightarrow & -36x \color{red}{+12} & = &12 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & -36x+5x& = &12-12 \\\Leftrightarrow & -31x& = &0 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{0}{ \color{red}{-31} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x+7)& = & -15 \color{red}{+} (5+4x) \\\Leftrightarrow & -3x+21& = &-15+5+4x \\\Leftrightarrow & -3x \color{red}{+21} & = &-10 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &-10 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & -3x-4x& = &-10-21 \\\Leftrightarrow & -7x& = &-31 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-31}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{31}{7} & & \\ & V = \left\{ \frac{31}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-3)& = & 2 \color{red}{+} (5+x) \\\Leftrightarrow & 8x-6& = &2+5+x \\\Leftrightarrow & 8x \color{red}{-6} & = &7 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 8x-x& = &7+6 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x+1)& = & 3 \color{red}{+} (14+x) \\\Leftrightarrow & -20x+5& = &3+14+x \\\Leftrightarrow & -20x \color{red}{+5} & = &17 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -20x-x& = &17-5 \\\Leftrightarrow & -21x& = &12 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{12}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)