Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-5x-6)& = & 14 \color{red}{+} (12+x) \\\Leftrightarrow & -20x-24& = &14+12+x \\\Leftrightarrow & -20x \color{red}{-24} & = &26 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &26 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -20x-x& = &26+24 \\\Leftrightarrow & -21x& = &50 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{50}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-50}{21} & & \\ & V = \left\{ \frac{-50}{21} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x+7)& = & 13 \color{red}{-} (-9+x) \\\Leftrightarrow & -6x+21& = &13+9-x \\\Leftrightarrow & -6x \color{red}{+21} & = &22 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -6x+x& = &22-21 \\\Leftrightarrow & -5x& = &1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-x-7)& = & 7 \color{red}{+} (-1+x) \\\Leftrightarrow & -2x-14& = &7-1+x \\\Leftrightarrow & -2x \color{red}{-14} & = &6 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -2x-x& = &6+14 \\\Leftrightarrow & -3x& = &20 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{20}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x+5)& = & 10 \color{red}{+} (15+x) \\\Leftrightarrow & 15x+15& = &10+15+x \\\Leftrightarrow & 15x \color{red}{+15} & = &25 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 15x-x& = &25-15 \\\Leftrightarrow & 14x& = &10 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{10}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{5}{7} & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x-5)& = & -4 \color{red}{-} (-12+x) \\\Leftrightarrow & -8x-10& = &-4+12-x \\\Leftrightarrow & -8x \color{red}{-10} & = &8 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -8x+x& = &8+10 \\\Leftrightarrow & -7x& = &18 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{18}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+2)& = & 7 \color{red}{-} (7+4x) \\\Leftrightarrow & -15x+10& = &7-7-4x \\\Leftrightarrow & -15x \color{red}{+10} & = &0 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &0 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & -15x+4x& = &0-10 \\\Leftrightarrow & -11x& = &-10 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-10}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x-5)& = & 1 \color{red}{-} (-15+3x) \\\Leftrightarrow & 5x-25& = &1+15-3x \\\Leftrightarrow & 5x \color{red}{-25} & = &16 \color{red}{-3x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+25} \\\Leftrightarrow & 5x+3x& = &16+25 \\\Leftrightarrow & 8x& = &41 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{41}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{41}{8} & & \\ & V = \left\{ \frac{41}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-2)& = & 6 \color{red}{+} (-11-5x) \\\Leftrightarrow & -6x-12& = &6-11-5x \\\Leftrightarrow & -6x \color{red}{-12} & = &-5 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & -6x+5x& = &-5+12 \\\Leftrightarrow & -x& = &7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{7}{ \color{red}{-1} } \\\Leftrightarrow & x = -7 & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x+2)& = & 1 \color{red}{+} (-2+x) \\\Leftrightarrow & 24x+8& = &1-2+x \\\Leftrightarrow & 24x \color{red}{+8} & = &-1 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 24x-x& = &-1-8 \\\Leftrightarrow & 23x& = &-9 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-9}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-9}{23} & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-2)& = & 12 \color{red}{+} (-9-3x) \\\Leftrightarrow & -4x-4& = &12-9-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &3 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &3+4 \\\Leftrightarrow & -x& = &7 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{7}{ \color{red}{-1} } \\\Leftrightarrow & x = -7 & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-x+4)& = & 8 \color{red}{-} (2-3x) \\\Leftrightarrow & -4x+16& = &8-2+3x \\\Leftrightarrow & -4x \color{red}{+16} & = &6 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & -4x-3x& = &6-16 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x-6)& = & -7 \color{red}{+} (7+x) \\\Leftrightarrow & 18x-18& = &-7+7+x \\\Leftrightarrow & 18x \color{red}{-18} & = &0 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &0+18 \\\Leftrightarrow & 17x& = &18 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{18}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{18}{17} & & \\ & V = \left\{ \frac{18}{17} \right\} & \\\end{align}\)