Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x-6)& = & -14 \color{red}{-} (12+x) \\\Leftrightarrow & -12x-18& = &-14-12-x \\\Leftrightarrow & -12x \color{red}{-18} & = &-26 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &-26+18 \\\Leftrightarrow & -11x& = &-8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x-6)& = & -1 \color{red}{+} (-1-2x) \\\Leftrightarrow & -3x-18& = &-1-1-2x \\\Leftrightarrow & -3x \color{red}{-18} & = &-2 \color{red}{-2x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &-2 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & -3x+2x& = &-2+18 \\\Leftrightarrow & -x& = &16 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{16}{ \color{red}{-1} } \\\Leftrightarrow & x = -16 & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-3)& = & 5 \color{red}{+} (9+x) \\\Leftrightarrow & 12x-9& = &5+9+x \\\Leftrightarrow & 12x \color{red}{-9} & = &14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 12x-x& = &14+9 \\\Leftrightarrow & 11x& = &23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x+1)& = & -5 \color{red}{+} (-12+x) \\\Leftrightarrow & 12x+6& = &-5-12+x \\\Leftrightarrow & 12x \color{red}{+6} & = &-17 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 12x-x& = &-17-6 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-2x-5)& = & 14 \color{red}{-} (14+x) \\\Leftrightarrow & -4x-10& = &14-14-x \\\Leftrightarrow & -4x \color{red}{-10} & = &0 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -4x+x& = &0+10 \\\Leftrightarrow & -3x& = &10 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{10}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x+4)& = & 2 \color{red}{+} (-5+3x) \\\Leftrightarrow & -4x+16& = &2-5+3x \\\Leftrightarrow & -4x \color{red}{+16} & = &-3 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & -4x-3x& = &-3-16 \\\Leftrightarrow & -7x& = &-19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{19}{7} & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (5x+4)& = & -14 \color{red}{+} (-8+x) \\\Leftrightarrow & 25x+20& = &-14-8+x \\\Leftrightarrow & 25x \color{red}{+20} & = &-22 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 25x-x& = &-22-20 \\\Leftrightarrow & 24x& = &-42 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-42}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-7}{4} & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x+7)& = & 7 \color{red}{-} (5+x) \\\Leftrightarrow & -6x+14& = &7-5-x \\\Leftrightarrow & -6x \color{red}{+14} & = &2 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -6x+x& = &2-14 \\\Leftrightarrow & -5x& = &-12 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-12}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{12}{5} & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x-7)& = & 9 \color{red}{+} (-12+x) \\\Leftrightarrow & -6x-42& = &9-12+x \\\Leftrightarrow & -6x \color{red}{-42} & = &-3 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -6x-x& = &-3+42 \\\Leftrightarrow & -7x& = &39 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{39}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-39}{7} & & \\ & V = \left\{ \frac{-39}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-5x+1)& = & -7 \color{red}{-} (11+4x) \\\Leftrightarrow & -15x+3& = &-7-11-4x \\\Leftrightarrow & -15x \color{red}{+3} & = &-18 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &-18 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & -15x+4x& = &-18-3 \\\Leftrightarrow & -11x& = &-21 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-21}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (2x+3)& = & -12 \color{red}{-} (3-5x) \\\Leftrightarrow & 6x+9& = &-12-3+5x \\\Leftrightarrow & 6x \color{red}{+9} & = &-15 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 6x-5x& = &-15-9 \\\Leftrightarrow & x& = &-24 \\ & V = \left\{ -24 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-x-2)& = & 10 \color{red}{+} (-2+3x) \\\Leftrightarrow & -5x-10& = &10-2+3x \\\Leftrightarrow & -5x \color{red}{-10} & = &8 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -5x-3x& = &8+10 \\\Leftrightarrow & -8x& = &18 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{18}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)