Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-2x-1)& = & 13 \color{red}{-} (-10+x) \\\Leftrightarrow & -8x-4& = &13+10-x \\\Leftrightarrow & -8x \color{red}{-4} & = &23 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -8x+x& = &23+4 \\\Leftrightarrow & -7x& = &27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x-2)& = & 15 \color{red}{-} (11+x) \\\Leftrightarrow & 6x-6& = &15-11-x \\\Leftrightarrow & 6x \color{red}{-6} & = &4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 6x+x& = &4+6 \\\Leftrightarrow & 7x& = &10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x-1)& = & 15 \color{red}{+} (-9+3x) \\\Leftrightarrow & 20x-4& = &15-9+3x \\\Leftrightarrow & 20x \color{red}{-4} & = &6 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 20x-3x& = &6+4 \\\Leftrightarrow & 17x& = &10 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{10}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{10}{17} & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (x-5)& = & 2 \color{red}{-} (2+x) \\\Leftrightarrow & 4x-20& = &2-2-x \\\Leftrightarrow & 4x \color{red}{-20} & = &0 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 4x+x& = &0+20 \\\Leftrightarrow & 5x& = &20 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{20}{ \color{red}{5} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (5x-1)& = & 1 \color{red}{+} (6-3x) \\\Leftrightarrow & 25x-5& = &1+6-3x \\\Leftrightarrow & 25x \color{red}{-5} & = &7 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 25x+3x& = &7+5 \\\Leftrightarrow & 28x& = &12 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{12}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (4x-6)& = & 12 \color{red}{-} (11+x) \\\Leftrightarrow & 8x-12& = &12-11-x \\\Leftrightarrow & 8x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 8x+x& = &1+12 \\\Leftrightarrow & 9x& = &13 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{13}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{13}{9} & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (5x-5)& = & -9 \color{red}{+} (14+x) \\\Leftrightarrow & 15x-15& = &-9+14+x \\\Leftrightarrow & 15x \color{red}{-15} & = &5 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 15x-x& = &5+15 \\\Leftrightarrow & 14x& = &20 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{20}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-3x+7)& = & -4 \color{red}{-} (4+x) \\\Leftrightarrow & -12x+28& = &-4-4-x \\\Leftrightarrow & -12x \color{red}{+28} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -12x+x& = &-8-28 \\\Leftrightarrow & -11x& = &-36 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-36}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{36}{11} & & \\ & V = \left\{ \frac{36}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+7)& = & -14 \color{red}{-} (-14+x) \\\Leftrightarrow & 3x+21& = &-14+14-x \\\Leftrightarrow & 3x \color{red}{+21} & = &0 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 3x+x& = &0-21 \\\Leftrightarrow & 4x& = &-21 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-21}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-21}{4} & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+2)& = & 6 \color{red}{+} (-5+x) \\\Leftrightarrow & -36x+12& = &6-5+x \\\Leftrightarrow & -36x \color{red}{+12} & = &1 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -36x-x& = &1-12 \\\Leftrightarrow & -37x& = &-11 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-11}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{11}{37} & & \\ & V = \left\{ \frac{11}{37} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x+7)& = & 2 \color{red}{-} (-1-5x) \\\Leftrightarrow & -6x+42& = &2+1+5x \\\Leftrightarrow & -6x \color{red}{+42} & = &3 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+42} \color{blue}{-42} \color{blue}{-5x} & = &3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-42} \\\Leftrightarrow & -6x-5x& = &3-42 \\\Leftrightarrow & -11x& = &-39 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-39}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{39}{11} & & \\ & V = \left\{ \frac{39}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x-3)& = & -11 \color{red}{+} (14+x) \\\Leftrightarrow & -6x-18& = &-11+14+x \\\Leftrightarrow & -6x \color{red}{-18} & = &3 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -6x-x& = &3+18 \\\Leftrightarrow & -7x& = &21 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{21}{ \color{red}{-7} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)