Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+5)& = & -2 \color{red}{-} (13-5x) \\\Leftrightarrow & 18x+30& = &-2-13+5x \\\Leftrightarrow & 18x \color{red}{+30} & = &-15 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+30} \color{blue}{-30} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-30} \\\Leftrightarrow & 18x-5x& = &-15-30 \\\Leftrightarrow & 13x& = &-45 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-45}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-45}{13} & & \\ & V = \left\{ \frac{-45}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x-5)& = & 3 \color{red}{-} (-1-5x) \\\Leftrightarrow & 36x-30& = &3+1+5x \\\Leftrightarrow & 36x \color{red}{-30} & = &4 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & 36x-5x& = &4+30 \\\Leftrightarrow & 31x& = &34 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{34}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{34}{31} & & \\ & V = \left\{ \frac{34}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x-1)& = & 8 \color{red}{+} (6-3x) \\\Leftrightarrow & 25x-5& = &8+6-3x \\\Leftrightarrow & 25x \color{red}{-5} & = &14 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 25x+3x& = &14+5 \\\Leftrightarrow & 28x& = &19 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{19}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{19}{28} & & \\ & V = \left\{ \frac{19}{28} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x-1)& = & -7 \color{red}{-} (-3+x) \\\Leftrightarrow & 12x-6& = &-7+3-x \\\Leftrightarrow & 12x \color{red}{-6} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &-4+6 \\\Leftrightarrow & 13x& = &2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x-6)& = & 5 \color{red}{-} (-13+x) \\\Leftrightarrow & 36x-36& = &5+13-x \\\Leftrightarrow & 36x \color{red}{-36} & = &18 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 36x+x& = &18+36 \\\Leftrightarrow & 37x& = &54 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{54}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{54}{37} & & \\ & V = \left\{ \frac{54}{37} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (2x-5)& = & -8 \color{red}{+} (15+x) \\\Leftrightarrow & 12x-30& = &-8+15+x \\\Leftrightarrow & 12x \color{red}{-30} & = &7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 12x-x& = &7+30 \\\Leftrightarrow & 11x& = &37 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{37}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{37}{11} & & \\ & V = \left\{ \frac{37}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x+4)& = & 5 \color{red}{+} (-4+x) \\\Leftrightarrow & 15x+20& = &5-4+x \\\Leftrightarrow & 15x \color{red}{+20} & = &1 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 15x-x& = &1-20 \\\Leftrightarrow & 14x& = &-19 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-19}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-19}{14} & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x+1)& = & 14 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x+4& = &14-7+x \\\Leftrightarrow & 12x \color{red}{+4} & = &7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & 12x-x& = &7-4 \\\Leftrightarrow & 11x& = &3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{3}{11} & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-5x+6)& = & 11 \color{red}{-} (12-2x) \\\Leftrightarrow & -15x+18& = &11-12+2x \\\Leftrightarrow & -15x \color{red}{+18} & = &-1 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & -15x-2x& = &-1-18 \\\Leftrightarrow & -17x& = &-19 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-19}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{19}{17} & & \\ & V = \left\{ \frac{19}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (3x+7)& = & -13 \color{red}{+} (3-2x) \\\Leftrightarrow & 9x+21& = &-13+3-2x \\\Leftrightarrow & 9x \color{red}{+21} & = &-10 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &-10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 9x+2x& = &-10-21 \\\Leftrightarrow & 11x& = &-31 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-31}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-31}{11} & & \\ & V = \left\{ \frac{-31}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x-1)& = & -14 \color{red}{+} (-3-2x) \\\Leftrightarrow & 15x-3& = &-14-3-2x \\\Leftrightarrow & 15x \color{red}{-3} & = &-17 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-17 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & 15x+2x& = &-17+3 \\\Leftrightarrow & 17x& = &-14 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-14}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-14}{17} & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x+4)& = & -7 \color{red}{+} (7-2x) \\\Leftrightarrow & -15x+12& = &-7+7-2x \\\Leftrightarrow & -15x \color{red}{+12} & = &0 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+12} \color{blue}{-12} \color{blue}{+2x} & = &0 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-12} \\\Leftrightarrow & -15x+2x& = &0-12 \\\Leftrightarrow & -13x& = &-12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{12}{13} & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)