Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-3x+4)& = & -12 \color{red}{-} (14+x) \\\Leftrightarrow & -9x+12& = &-12-14-x \\\Leftrightarrow & -9x \color{red}{+12} & = &-26 \color{red}{-x} \\\Leftrightarrow & -9x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -9x+x& = &-26-12 \\\Leftrightarrow & -8x& = &-38 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-38}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{19}{4} & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-3x-4)& = & -10 \color{red}{+} (2+4x) \\\Leftrightarrow & -9x-12& = &-10+2+4x \\\Leftrightarrow & -9x \color{red}{-12} & = &-8 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{-4x} & = &-8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+12} \\\Leftrightarrow & -9x-4x& = &-8+12 \\\Leftrightarrow & -13x& = &4 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{4}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x+4)& = & -14 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x+16& = &-14-1+x \\\Leftrightarrow & 12x \color{red}{+16} & = &-15 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 12x-x& = &-15-16 \\\Leftrightarrow & 11x& = &-31 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-31}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-31}{11} & & \\ & V = \left\{ \frac{-31}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-6)& = & -2 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x-18& = &-2+4-x \\\Leftrightarrow & -12x \color{red}{-18} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -12x+x& = &2+18 \\\Leftrightarrow & -11x& = &20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x+3)& = & -12 \color{red}{-} (-9+x) \\\Leftrightarrow & -6x+18& = &-12+9-x \\\Leftrightarrow & -6x \color{red}{+18} & = &-3 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &-3-18 \\\Leftrightarrow & -5x& = &-21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{21}{5} & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (x+5)& = & -4 \color{red}{-} (2-4x) \\\Leftrightarrow & 5x+25& = &-4-2+4x \\\Leftrightarrow & 5x \color{red}{+25} & = &-6 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{-4x} & = &-6 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-25} \\\Leftrightarrow & 5x-4x& = &-6-25 \\\Leftrightarrow & x& = &-31 \\ & V = \left\{ -31 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-2)& = & 1 \color{red}{+} (-1+x) \\\Leftrightarrow & 8x-8& = &1-1+x \\\Leftrightarrow & 8x \color{red}{-8} & = &0 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 8x-x& = &0+8 \\\Leftrightarrow & 7x& = &8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x-3)& = & -13 \color{red}{-} (2+x) \\\Leftrightarrow & 4x-6& = &-13-2-x \\\Leftrightarrow & 4x \color{red}{-6} & = &-15 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 4x+x& = &-15+6 \\\Leftrightarrow & 5x& = &-9 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-9}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-9}{5} & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x-7)& = & -10 \color{red}{+} (4+x) \\\Leftrightarrow & 12x-21& = &-10+4+x \\\Leftrightarrow & 12x \color{red}{-21} & = &-6 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 12x-x& = &-6+21 \\\Leftrightarrow & 11x& = &15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (5x-1)& = & 5 \color{red}{+} (-13+x) \\\Leftrightarrow & 25x-5& = &5-13+x \\\Leftrightarrow & 25x \color{red}{-5} & = &-8 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 25x-x& = &-8+5 \\\Leftrightarrow & 24x& = &-3 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-3}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (6x+2)& = & 10 \color{red}{+} (11-5x) \\\Leftrightarrow & 18x+6& = &10+11-5x \\\Leftrightarrow & 18x \color{red}{+6} & = &21 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 18x+5x& = &21-6 \\\Leftrightarrow & 23x& = &15 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{15}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x+7)& = & 11 \color{red}{-} (-3+3x) \\\Leftrightarrow & -2x+14& = &11+3-3x \\\Leftrightarrow & -2x \color{red}{+14} & = &14 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -2x+3x& = &14-14 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)