Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x+1)& = & -12 \color{red}{-} (14+x) \\\Leftrightarrow & -5x+5& = &-12-14-x \\\Leftrightarrow & -5x \color{red}{+5} & = &-26 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &-26 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -5x+x& = &-26-5 \\\Leftrightarrow & -4x& = &-31 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-31}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{31}{4} & & \\ & V = \left\{ \frac{31}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+5)& = & 6 \color{red}{+} (1+x) \\\Leftrightarrow & 6x+15& = &6+1+x \\\Leftrightarrow & 6x \color{red}{+15} & = &7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 6x-x& = &7-15 \\\Leftrightarrow & 5x& = &-8 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-8}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (4x-5)& = & 6 \color{red}{+} (6+x) \\\Leftrightarrow & 12x-15& = &6+6+x \\\Leftrightarrow & 12x \color{red}{-15} & = &12 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 12x-x& = &12+15 \\\Leftrightarrow & 11x& = &27 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{27}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{27}{11} & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x-2)& = & -4 \color{red}{+} (14-5x) \\\Leftrightarrow & 18x-12& = &-4+14-5x \\\Leftrightarrow & 18x \color{red}{-12} & = &10 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 18x+5x& = &10+12 \\\Leftrightarrow & 23x& = &22 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{22}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{22}{23} & & \\ & V = \left\{ \frac{22}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (6x+1)& = & 6 \color{red}{-} (13+x) \\\Leftrightarrow & 24x+4& = &6-13-x \\\Leftrightarrow & 24x \color{red}{+4} & = &-7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 24x+x& = &-7-4 \\\Leftrightarrow & 25x& = &-11 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-11}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-11}{25} & & \\ & V = \left\{ \frac{-11}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-4x-5)& = & 8 \color{red}{+} (-14+x) \\\Leftrightarrow & -12x-15& = &8-14+x \\\Leftrightarrow & -12x \color{red}{-15} & = &-6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -12x-x& = &-6+15 \\\Leftrightarrow & -13x& = &9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-9}{13} & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (5x-4)& = & -3 \color{red}{+} (-5+x) \\\Leftrightarrow & 10x-8& = &-3-5+x \\\Leftrightarrow & 10x \color{red}{-8} & = &-8 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 10x-x& = &-8+8 \\\Leftrightarrow & 9x& = &0 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{0}{ \color{red}{9} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x-2)& = & 10 \color{red}{+} (-3+x) \\\Leftrightarrow & 15x-6& = &10-3+x \\\Leftrightarrow & 15x \color{red}{-6} & = &7 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 15x-x& = &7+6 \\\Leftrightarrow & 14x& = &13 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{13}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{13}{14} & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-3x-4)& = & 15 \color{red}{-} (-5+2x) \\\Leftrightarrow & -9x-12& = &15+5-2x \\\Leftrightarrow & -9x \color{red}{-12} & = &20 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -9x+2x& = &20+12 \\\Leftrightarrow & -7x& = &32 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{32}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-32}{7} & & \\ & V = \left\{ \frac{-32}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x-4)& = & -10 \color{red}{-} (1-2x) \\\Leftrightarrow & 15x-12& = &-10-1+2x \\\Leftrightarrow & 15x \color{red}{-12} & = &-11 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & 15x-2x& = &-11+12 \\\Leftrightarrow & 13x& = &1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+6)& = & -4 \color{red}{-} (-7+3x) \\\Leftrightarrow & -4x+12& = &-4+7-3x \\\Leftrightarrow & -4x \color{red}{+12} & = &3 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & -4x+3x& = &3-12 \\\Leftrightarrow & -x& = &-9 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-9}{ \color{red}{-1} } \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x-5)& = & -14 \color{red}{+} (4+x) \\\Leftrightarrow & -24x-20& = &-14+4+x \\\Leftrightarrow & -24x \color{red}{-20} & = &-10 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -24x-x& = &-10+20 \\\Leftrightarrow & -25x& = &10 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{10}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)