Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x-3)& = & 2 \color{red}{+} (-1+x) \\\Leftrightarrow & 3x-9& = &2-1+x \\\Leftrightarrow & 3x \color{red}{-9} & = &1 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 3x-x& = &1+9 \\\Leftrightarrow & 2x& = &10 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{10}{ \color{red}{2} } \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x-6)& = & 11 \color{red}{-} (9+x) \\\Leftrightarrow & 10x-30& = &11-9-x \\\Leftrightarrow & 10x \color{red}{-30} & = &2 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 10x+x& = &2+30 \\\Leftrightarrow & 11x& = &32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x-7)& = & -2 \color{red}{+} (14+3x) \\\Leftrightarrow & -2x-14& = &-2+14+3x \\\Leftrightarrow & -2x \color{red}{-14} & = &12 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+14} \\\Leftrightarrow & -2x-3x& = &12+14 \\\Leftrightarrow & -5x& = &26 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{26}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-26}{5} & & \\ & V = \left\{ \frac{-26}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (4x+7)& = & -14 \color{red}{+} (-12+x) \\\Leftrightarrow & 24x+42& = &-14-12+x \\\Leftrightarrow & 24x \color{red}{+42} & = &-26 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 24x-x& = &-26-42 \\\Leftrightarrow & 23x& = &-68 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-68}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-68}{23} & & \\ & V = \left\{ \frac{-68}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x-6)& = & 9 \color{red}{-} (2+x) \\\Leftrightarrow & 6x-18& = &9-2-x \\\Leftrightarrow & 6x \color{red}{-18} & = &7 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 6x+x& = &7+18 \\\Leftrightarrow & 7x& = &25 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{25}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{25}{7} & & \\ & V = \left\{ \frac{25}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x+2)& = & 14 \color{red}{-} (-9+x) \\\Leftrightarrow & -30x+10& = &14+9-x \\\Leftrightarrow & -30x \color{red}{+10} & = &23 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -30x+x& = &23-10 \\\Leftrightarrow & -29x& = &13 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{13}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-13}{29} & & \\ & V = \left\{ \frac{-13}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x-1)& = & -5 \color{red}{-} (6-2x) \\\Leftrightarrow & 15x-5& = &-5-6+2x \\\Leftrightarrow & 15x \color{red}{-5} & = &-11 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &-11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 15x-2x& = &-11+5 \\\Leftrightarrow & 13x& = &-6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x-6)& = & -12 \color{red}{+} (-15-5x) \\\Leftrightarrow & -6x-18& = &-12-15-5x \\\Leftrightarrow & -6x \color{red}{-18} & = &-27 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &-27 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -6x+5x& = &-27+18 \\\Leftrightarrow & -x& = &-9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-9}{ \color{red}{-1} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-4x+2)& = & 13 \color{red}{+} (2+x) \\\Leftrightarrow & -24x+12& = &13+2+x \\\Leftrightarrow & -24x \color{red}{+12} & = &15 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &15-12 \\\Leftrightarrow & -25x& = &3 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{3}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-3}{25} & & \\ & V = \left\{ \frac{-3}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x-7)& = & 5 \color{red}{-} (9+2x) \\\Leftrightarrow & 3x-21& = &5-9-2x \\\Leftrightarrow & 3x \color{red}{-21} & = &-4 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{+2x} & = &-4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+21} \\\Leftrightarrow & 3x+2x& = &-4+21 \\\Leftrightarrow & 5x& = &17 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{17}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{17}{5} & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-2x-7)& = & -1 \color{red}{-} (-11+x) \\\Leftrightarrow & -8x-28& = &-1+11-x \\\Leftrightarrow & -8x \color{red}{-28} & = &10 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -8x+x& = &10+28 \\\Leftrightarrow & -7x& = &38 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{38}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-38}{7} & & \\ & V = \left\{ \frac{-38}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x-5)& = & 11 \color{red}{-} (1+x) \\\Leftrightarrow & 4x-20& = &11-1-x \\\Leftrightarrow & 4x \color{red}{-20} & = &10 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 4x+x& = &10+20 \\\Leftrightarrow & 5x& = &30 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{30}{ \color{red}{5} } \\\Leftrightarrow & x = 6 & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)