Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (x+7)& = & 5 \color{red}{-} (-2+3x) \\\Leftrightarrow & 2x+14& = &5+2-3x \\\Leftrightarrow & 2x \color{red}{+14} & = &7 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & 2x+3x& = &7-14 \\\Leftrightarrow & 5x& = &-7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x+7)& = & -3 \color{red}{-} (1-5x) \\\Leftrightarrow & -6x+21& = &-3-1+5x \\\Leftrightarrow & -6x \color{red}{+21} & = &-4 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & -6x-5x& = &-4-21 \\\Leftrightarrow & -11x& = &-25 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-25}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x-7)& = & 8 \color{red}{-} (-11+x) \\\Leftrightarrow & 15x-35& = &8+11-x \\\Leftrightarrow & 15x \color{red}{-35} & = &19 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 15x+x& = &19+35 \\\Leftrightarrow & 16x& = &54 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{54}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{27}{8} & & \\ & V = \left\{ \frac{27}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x+5)& = & -12 \color{red}{-} (10-3x) \\\Leftrightarrow & 10x+25& = &-12-10+3x \\\Leftrightarrow & 10x \color{red}{+25} & = &-22 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{-3x} & = &-22 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-25} \\\Leftrightarrow & 10x-3x& = &-22-25 \\\Leftrightarrow & 7x& = &-47 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-47}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-47}{7} & & \\ & V = \left\{ \frac{-47}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (3x+4)& = & 6 \color{red}{-} (15+x) \\\Leftrightarrow & 6x+8& = &6-15-x \\\Leftrightarrow & 6x \color{red}{+8} & = &-9 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 6x+x& = &-9-8 \\\Leftrightarrow & 7x& = &-17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-1)& = & -15 \color{red}{-} (7+x) \\\Leftrightarrow & -6x-6& = &-15-7-x \\\Leftrightarrow & -6x \color{red}{-6} & = &-22 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &-22+6 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x+2)& = & 13 \color{red}{-} (-13+x) \\\Leftrightarrow & 18x+12& = &13+13-x \\\Leftrightarrow & 18x \color{red}{+12} & = &26 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &26 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &26-12 \\\Leftrightarrow & 19x& = &14 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{14}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{14}{19} & & \\ & V = \left\{ \frac{14}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x+1)& = & -3 \color{red}{-} (-2+x) \\\Leftrightarrow & 12x+6& = &-3+2-x \\\Leftrightarrow & 12x \color{red}{+6} & = &-1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &-1-6 \\\Leftrightarrow & 13x& = &-7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-7}{13} & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x+4)& = & 9 \color{red}{+} (-11+2x) \\\Leftrightarrow & 25x+20& = &9-11+2x \\\Leftrightarrow & 25x \color{red}{+20} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & 25x-2x& = &-2-20 \\\Leftrightarrow & 23x& = &-22 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-22}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-x-1)& = & -15 \color{red}{+} (-5+x) \\\Leftrightarrow & -4x-4& = &-15-5+x \\\Leftrightarrow & -4x \color{red}{-4} & = &-20 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -4x-x& = &-20+4 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x+2)& = & -6 \color{red}{+} (14+x) \\\Leftrightarrow & 15x+6& = &-6+14+x \\\Leftrightarrow & 15x \color{red}{+6} & = &8 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 15x-x& = &8-6 \\\Leftrightarrow & 14x& = &2 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{2}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+7)& = & -10 \color{red}{-} (-4-2x) \\\Leftrightarrow & -15x+35& = &-10+4+2x \\\Leftrightarrow & -15x \color{red}{+35} & = &-6 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{-2x} & = &-6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-35} \\\Leftrightarrow & -15x-2x& = &-6-35 \\\Leftrightarrow & -17x& = &-41 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-41}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{41}{17} & & \\ & V = \left\{ \frac{41}{17} \right\} & \\\end{align}\)