Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (6x+2)& = & -11 \color{red}{+} (2+x) \\\Leftrightarrow & 12x+4& = &-11+2+x \\\Leftrightarrow & 12x \color{red}{+4} & = &-9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &-9-4 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (5x+2)& = & 5 \color{red}{+} (9+x) \\\Leftrightarrow & 15x+6& = &5+9+x \\\Leftrightarrow & 15x \color{red}{+6} & = &14 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 15x-x& = &14-6 \\\Leftrightarrow & 14x& = &8 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{8}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-4x+1)& = & 14 \color{red}{+} (-12+x) \\\Leftrightarrow & -12x+3& = &14-12+x \\\Leftrightarrow & -12x \color{red}{+3} & = &2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & -12x-x& = &2-3 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x+2)& = & -4 \color{red}{-} (-1+x) \\\Leftrightarrow & -20x+8& = &-4+1-x \\\Leftrightarrow & -20x \color{red}{+8} & = &-3 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -20x+x& = &-3-8 \\\Leftrightarrow & -19x& = &-11 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-11}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{11}{19} & & \\ & V = \left\{ \frac{11}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x+3)& = & 5 \color{red}{-} (-7+x) \\\Leftrightarrow & -8x+12& = &5+7-x \\\Leftrightarrow & -8x \color{red}{+12} & = &12 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -8x+x& = &12-12 \\\Leftrightarrow & -7x& = &0 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{0}{ \color{red}{-7} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+3)& = & -3 \color{red}{+} (15+x) \\\Leftrightarrow & 24x+18& = &-3+15+x \\\Leftrightarrow & 24x \color{red}{+18} & = &12 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 24x-x& = &12-18 \\\Leftrightarrow & 23x& = &-6 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-6}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (x-4)& = & 14 \color{red}{-} (-6+x) \\\Leftrightarrow & 2x-8& = &14+6-x \\\Leftrightarrow & 2x \color{red}{-8} & = &20 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 2x+x& = &20+8 \\\Leftrightarrow & 3x& = &28 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{28}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{28}{3} & & \\ & V = \left\{ \frac{28}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x-2)& = & 14 \color{red}{-} (-2-4x) \\\Leftrightarrow & -9x-6& = &14+2+4x \\\Leftrightarrow & -9x \color{red}{-6} & = &16 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{-4x} & = &16 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+6} \\\Leftrightarrow & -9x-4x& = &16+6 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-3x-2)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & -18x-12& = &8-4+x \\\Leftrightarrow & -18x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -18x-x& = &4+12 \\\Leftrightarrow & -19x& = &16 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{16}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x-7)& = & 2 \color{red}{-} (-11-5x) \\\Leftrightarrow & -8x-28& = &2+11+5x \\\Leftrightarrow & -8x \color{red}{-28} & = &13 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+28} \\\Leftrightarrow & -8x-5x& = &13+28 \\\Leftrightarrow & -13x& = &41 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{41}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-41}{13} & & \\ & V = \left\{ \frac{-41}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x+6)& = & -11 \color{red}{-} (2+x) \\\Leftrightarrow & 30x+30& = &-11-2-x \\\Leftrightarrow & 30x \color{red}{+30} & = &-13 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &-13-30 \\\Leftrightarrow & 31x& = &-43 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-43}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-43}{31} & & \\ & V = \left\{ \frac{-43}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (3x-1)& = & -1 \color{red}{-} (-9-5x) \\\Leftrightarrow & 6x-2& = &-1+9+5x \\\Leftrightarrow & 6x \color{red}{-2} & = &8 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+2} \\\Leftrightarrow & 6x-5x& = &8+2 \\\Leftrightarrow & x& = &10 \\ & V = \left\{ 10 \right\} & \\\end{align}\)