Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x-1)& = & 13 \color{red}{+} (14+4x) \\\Leftrightarrow & 5x-5& = &13+14+4x \\\Leftrightarrow & 5x \color{red}{-5} & = &27 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &27 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & 5x-4x& = &27+5 \\\Leftrightarrow & x& = &32 \\ & V = \left\{ 32 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x+2)& = & 11 \color{red}{+} (3+2x) \\\Leftrightarrow & -3x+6& = &11+3+2x \\\Leftrightarrow & -3x \color{red}{+6} & = &14 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &14 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & -3x-2x& = &14-6 \\\Leftrightarrow & -5x& = &8 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{8}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x+2)& = & 7 \color{red}{-} (-5-3x) \\\Leftrightarrow & -4x+8& = &7+5+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &12 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &12-8 \\\Leftrightarrow & -7x& = &4 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{4}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-3x-3)& = & 14 \color{red}{+} (-8+x) \\\Leftrightarrow & -15x-15& = &14-8+x \\\Leftrightarrow & -15x \color{red}{-15} & = &6 \color{red}{+x} \\\Leftrightarrow & -15x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -15x-x& = &6+15 \\\Leftrightarrow & -16x& = &21 \\\Leftrightarrow & \frac{-16x}{ \color{red}{-16} }& = &\frac{21}{ \color{red}{-16} } \\\Leftrightarrow & x = \frac{-21}{16} & & \\ & V = \left\{ \frac{-21}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x-2)& = & 13 \color{red}{+} (-7+x) \\\Leftrightarrow & 18x-6& = &13-7+x \\\Leftrightarrow & 18x \color{red}{-6} & = &6 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &6+6 \\\Leftrightarrow & 17x& = &12 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{12}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{12}{17} & & \\ & V = \left\{ \frac{12}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-6x+2)& = & 14 \color{red}{+} (-5+x) \\\Leftrightarrow & -30x+10& = &14-5+x \\\Leftrightarrow & -30x \color{red}{+10} & = &9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -30x-x& = &9-10 \\\Leftrightarrow & -31x& = &-1 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-1}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{1}{31} & & \\ & V = \left\{ \frac{1}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x+4)& = & -5 \color{red}{+} (6+x) \\\Leftrightarrow & 30x+20& = &-5+6+x \\\Leftrightarrow & 30x \color{red}{+20} & = &1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 30x-x& = &1-20 \\\Leftrightarrow & 29x& = &-19 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-19}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-19}{29} & & \\ & V = \left\{ \frac{-19}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-2x-3)& = & 8 \color{red}{-} (-10-5x) \\\Leftrightarrow & -8x-12& = &8+10+5x \\\Leftrightarrow & -8x \color{red}{-12} & = &18 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -8x-5x& = &18+12 \\\Leftrightarrow & -13x& = &30 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{30}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-30}{13} & & \\ & V = \left\{ \frac{-30}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x-2)& = & -15 \color{red}{+} (3+2x) \\\Leftrightarrow & -3x-6& = &-15+3+2x \\\Leftrightarrow & -3x \color{red}{-6} & = &-12 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+6} \\\Leftrightarrow & -3x-2x& = &-12+6 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x-2)& = & -15 \color{red}{+} (1-5x) \\\Leftrightarrow & 6x-6& = &-15+1-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-14 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-14 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &-14+6 \\\Leftrightarrow & 11x& = &-8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x+1)& = & -2 \color{red}{-} (6+x) \\\Leftrightarrow & 6x+2& = &-2-6-x \\\Leftrightarrow & 6x \color{red}{+2} & = &-8 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 6x+x& = &-8-2 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (6x+3)& = & -3 \color{red}{-} (12+x) \\\Leftrightarrow & 12x+6& = &-3-12-x \\\Leftrightarrow & 12x \color{red}{+6} & = &-15 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-15 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &-15-6 \\\Leftrightarrow & 13x& = &-21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-21}{13} & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)