Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (2x-7)& = & 3 \color{red}{+} (-9+x) \\\Leftrightarrow & 8x-28& = &3-9+x \\\Leftrightarrow & 8x \color{red}{-28} & = &-6 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 8x-x& = &-6+28 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x+1)& = & -14 \color{red}{-} (-10-2x) \\\Leftrightarrow & -3x+3& = &-14+10+2x \\\Leftrightarrow & -3x \color{red}{+3} & = &-4 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-3} \\\Leftrightarrow & -3x-2x& = &-4-3 \\\Leftrightarrow & -5x& = &-7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{7}{5} & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (2x-3)& = & 9 \color{red}{-} (-11+3x) \\\Leftrightarrow & 10x-15& = &9+11-3x \\\Leftrightarrow & 10x \color{red}{-15} & = &20 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &20 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & 10x+3x& = &20+15 \\\Leftrightarrow & 13x& = &35 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{35}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{35}{13} & & \\ & V = \left\{ \frac{35}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (5x+4)& = & -1 \color{red}{-} (14+x) \\\Leftrightarrow & 30x+24& = &-1-14-x \\\Leftrightarrow & 30x \color{red}{+24} & = &-15 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 30x+x& = &-15-24 \\\Leftrightarrow & 31x& = &-39 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-39}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-39}{31} & & \\ & V = \left\{ \frac{-39}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x-3)& = & -11 \color{red}{-} (7+x) \\\Leftrightarrow & -6x-18& = &-11-7-x \\\Leftrightarrow & -6x \color{red}{-18} & = &-18 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -6x+x& = &-18+18 \\\Leftrightarrow & -5x& = &0 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{0}{ \color{red}{-5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (5x-2)& = & -11 \color{red}{+} (4+x) \\\Leftrightarrow & 20x-8& = &-11+4+x \\\Leftrightarrow & 20x \color{red}{-8} & = &-7 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 20x-x& = &-7+8 \\\Leftrightarrow & 19x& = &1 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{1}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{1}{19} & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+3)& = & -13 \color{red}{-} (-3+x) \\\Leftrightarrow & -30x+15& = &-13+3-x \\\Leftrightarrow & -30x \color{red}{+15} & = &-10 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -30x+x& = &-10-15 \\\Leftrightarrow & -29x& = &-25 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-25}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{25}{29} & & \\ & V = \left\{ \frac{25}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (2x+1)& = & -3 \color{red}{-} (12+x) \\\Leftrightarrow & 8x+4& = &-3-12-x \\\Leftrightarrow & 8x \color{red}{+4} & = &-15 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 8x+x& = &-15-4 \\\Leftrightarrow & 9x& = &-19 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-19}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-19}{9} & & \\ & V = \left\{ \frac{-19}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x+4)& = & 2 \color{red}{-} (-7-3x) \\\Leftrightarrow & 10x+8& = &2+7+3x \\\Leftrightarrow & 10x \color{red}{+8} & = &9 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 10x-3x& = &9-8 \\\Leftrightarrow & 7x& = &1 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{1}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x-1)& = & -15 \color{red}{+} (4+x) \\\Leftrightarrow & -8x-4& = &-15+4+x \\\Leftrightarrow & -8x \color{red}{-4} & = &-11 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -8x-x& = &-11+4 \\\Leftrightarrow & -9x& = &-7 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-7}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{7}{9} & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-5x-2)& = & -15 \color{red}{-} (-15-2x) \\\Leftrightarrow & -15x-6& = &-15+15+2x \\\Leftrightarrow & -15x \color{red}{-6} & = &0 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &0 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -15x-2x& = &0+6 \\\Leftrightarrow & -17x& = &6 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{6}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+1)& = & 6 \color{red}{-} (7+x) \\\Leftrightarrow & 30x+5& = &6-7-x \\\Leftrightarrow & 30x \color{red}{+5} & = &-1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & 30x+x& = &-1-5 \\\Leftrightarrow & 31x& = &-6 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-6}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-6}{31} & & \\ & V = \left\{ \frac{-6}{31} \right\} & \\\end{align}\)