Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (3x-7)& = & 11 \color{red}{+} (-6+x) \\\Leftrightarrow & 12x-28& = &11-6+x \\\Leftrightarrow & 12x \color{red}{-28} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 12x-x& = &5+28 \\\Leftrightarrow & 11x& = &33 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{33}{ \color{red}{11} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (3x+7)& = & -2 \color{red}{-} (-4+x) \\\Leftrightarrow & 6x+14& = &-2+4-x \\\Leftrightarrow & 6x \color{red}{+14} & = &2 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 6x+x& = &2-14 \\\Leftrightarrow & 7x& = &-12 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-12}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-12}{7} & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x-3)& = & -13 \color{red}{-} (-3-5x) \\\Leftrightarrow & 6x-6& = &-13+3+5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-10 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 6x-5x& = &-10+6 \\\Leftrightarrow & x& = &-4 \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x+3)& = & 10 \color{red}{+} (-6-5x) \\\Leftrightarrow & -6x+18& = &10-6-5x \\\Leftrightarrow & -6x \color{red}{+18} & = &4 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-18} \\\Leftrightarrow & -6x+5x& = &4-18 \\\Leftrightarrow & -x& = &-14 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-14}{ \color{red}{-1} } \\\Leftrightarrow & x = 14 & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x+7)& = & 3 \color{red}{+} (14-5x) \\\Leftrightarrow & -36x+42& = &3+14-5x \\\Leftrightarrow & -36x \color{red}{+42} & = &17 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -36x+5x& = &17-42 \\\Leftrightarrow & -31x& = &-25 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-25}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{25}{31} & & \\ & V = \left\{ \frac{25}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-2)& = & 11 \color{red}{+} (3+x) \\\Leftrightarrow & 18x-6& = &11+3+x \\\Leftrightarrow & 18x \color{red}{-6} & = &14 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &14+6 \\\Leftrightarrow & 17x& = &20 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{20}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{20}{17} & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x+3)& = & 2 \color{red}{-} (11+x) \\\Leftrightarrow & 30x+18& = &2-11-x \\\Leftrightarrow & 30x \color{red}{+18} & = &-9 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 30x+x& = &-9-18 \\\Leftrightarrow & 31x& = &-27 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-27}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-27}{31} & & \\ & V = \left\{ \frac{-27}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-3x+3)& = & -13 \color{red}{-} (-6+x) \\\Leftrightarrow & -18x+18& = &-13+6-x \\\Leftrightarrow & -18x \color{red}{+18} & = &-7 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -18x+x& = &-7-18 \\\Leftrightarrow & -17x& = &-25 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-25}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{25}{17} & & \\ & V = \left\{ \frac{25}{17} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (3x-4)& = & -4 \color{red}{+} (-9+x) \\\Leftrightarrow & 18x-24& = &-4-9+x \\\Leftrightarrow & 18x \color{red}{-24} & = &-13 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 18x-x& = &-13+24 \\\Leftrightarrow & 17x& = &11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x+7)& = & 7 \color{red}{-} (-6-5x) \\\Leftrightarrow & -8x+14& = &7+6+5x \\\Leftrightarrow & -8x \color{red}{+14} & = &13 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+14} \color{blue}{-14} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-14} \\\Leftrightarrow & -8x-5x& = &13-14 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x-1)& = & 13 \color{red}{-} (11+x) \\\Leftrightarrow & 30x-5& = &13-11-x \\\Leftrightarrow & 30x \color{red}{-5} & = &2 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 30x+x& = &2+5 \\\Leftrightarrow & 31x& = &7 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{7}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{7}{31} & & \\ & V = \left\{ \frac{7}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (6x-5)& = & -5 \color{red}{+} (-6+x) \\\Leftrightarrow & 36x-30& = &-5-6+x \\\Leftrightarrow & 36x \color{red}{-30} & = &-11 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 36x-x& = &-11+30 \\\Leftrightarrow & 35x& = &19 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{19}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{19}{35} & & \\ & V = \left\{ \frac{19}{35} \right\} & \\\end{align}\)