Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+1)& = & 13 \color{red}{-} (12-3x) \\\Leftrightarrow & 25x+5& = &13-12+3x \\\Leftrightarrow & 25x \color{red}{+5} & = &1 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & 25x-3x& = &1-5 \\\Leftrightarrow & 22x& = &-4 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{-4}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-5x-7)& = & 14 \color{red}{-} (2+x) \\\Leftrightarrow & -30x-42& = &14-2-x \\\Leftrightarrow & -30x \color{red}{-42} & = &12 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -30x+x& = &12+42 \\\Leftrightarrow & -29x& = &54 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{54}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-54}{29} & & \\ & V = \left\{ \frac{-54}{29} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-3x+7)& = & 15 \color{red}{-} (-11-5x) \\\Leftrightarrow & -6x+14& = &15+11+5x \\\Leftrightarrow & -6x \color{red}{+14} & = &26 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+14} \color{blue}{-14} \color{blue}{-5x} & = &26 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-14} \\\Leftrightarrow & -6x-5x& = &26-14 \\\Leftrightarrow & -11x& = &12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x-7)& = & 10 \color{red}{-} (3+x) \\\Leftrightarrow & 12x-21& = &10-3-x \\\Leftrightarrow & 12x \color{red}{-21} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+21} \\\Leftrightarrow & 12x+x& = &7+21 \\\Leftrightarrow & 13x& = &28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x-3)& = & -15 \color{red}{-} (5+x) \\\Leftrightarrow & -36x-18& = &-15-5-x \\\Leftrightarrow & -36x \color{red}{-18} & = &-20 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -36x+x& = &-20+18 \\\Leftrightarrow & -35x& = &-2 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-2}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (3x+6)& = & 10 \color{red}{+} (-4+x) \\\Leftrightarrow & 15x+30& = &10-4+x \\\Leftrightarrow & 15x \color{red}{+30} & = &6 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 15x-x& = &6-30 \\\Leftrightarrow & 14x& = &-24 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-24}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-3x+7)& = & 6 \color{red}{+} (11+x) \\\Leftrightarrow & -18x+42& = &6+11+x \\\Leftrightarrow & -18x \color{red}{+42} & = &17 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -18x-x& = &17-42 \\\Leftrightarrow & -19x& = &-25 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-25}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{25}{19} & & \\ & V = \left\{ \frac{25}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-4)& = & 14 \color{red}{+} (-14+2x) \\\Leftrightarrow & -9x-12& = &14-14+2x \\\Leftrightarrow & -9x \color{red}{-12} & = &0 \color{red}{+2x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & -9x-2x& = &0+12 \\\Leftrightarrow & -11x& = &12 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{12}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-2x+3)& = & 14 \color{red}{+} (-8+x) \\\Leftrightarrow & -6x+9& = &14-8+x \\\Leftrightarrow & -6x \color{red}{+9} & = &6 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -6x-x& = &6-9 \\\Leftrightarrow & -7x& = &-3 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-3}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x-5)& = & -11 \color{red}{+} (4+4x) \\\Leftrightarrow & -5x-25& = &-11+4+4x \\\Leftrightarrow & -5x \color{red}{-25} & = &-7 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-25} \color{blue}{+25} \color{blue}{-4x} & = &-7 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+25} \\\Leftrightarrow & -5x-4x& = &-7+25 \\\Leftrightarrow & -9x& = &18 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{18}{ \color{red}{-9} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-6)& = & -2 \color{red}{-} (8-2x) \\\Leftrightarrow & -3x-18& = &-2-8+2x \\\Leftrightarrow & -3x \color{red}{-18} & = &-10 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &-10 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & -3x-2x& = &-10+18 \\\Leftrightarrow & -5x& = &8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-5x+2)& = & -9 \color{red}{+} (11+x) \\\Leftrightarrow & -20x+8& = &-9+11+x \\\Leftrightarrow & -20x \color{red}{+8} & = &2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -20x-x& = &2-8 \\\Leftrightarrow & -21x& = &-6 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-6}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)