Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-x+6)& = & -6 \color{red}{+} (-14+x) \\\Leftrightarrow & -4x+24& = &-6-14+x \\\Leftrightarrow & -4x \color{red}{+24} & = &-20 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -4x-x& = &-20-24 \\\Leftrightarrow & -5x& = &-44 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-44}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{44}{5} & & \\ & V = \left\{ \frac{44}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (5x-5)& = & 10 \color{red}{-} (3-2x) \\\Leftrightarrow & 25x-25& = &10-3+2x \\\Leftrightarrow & 25x \color{red}{-25} & = &7 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{-25} \color{blue}{+25} \color{blue}{-2x} & = &7 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+25} \\\Leftrightarrow & 25x-2x& = &7+25 \\\Leftrightarrow & 23x& = &32 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{32}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{32}{23} & & \\ & V = \left\{ \frac{32}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-5x+5)& = & 14 \color{red}{+} (-6+3x) \\\Leftrightarrow & -10x+10& = &14-6+3x \\\Leftrightarrow & -10x \color{red}{+10} & = &8 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -10x-3x& = &8-10 \\\Leftrightarrow & -13x& = &-2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-4x-6)& = & 15 \color{red}{+} (-10+x) \\\Leftrightarrow & -24x-36& = &15-10+x \\\Leftrightarrow & -24x \color{red}{-36} & = &5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -24x-x& = &5+36 \\\Leftrightarrow & -25x& = &41 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{41}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-41}{25} & & \\ & V = \left\{ \frac{-41}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-x+4)& = & 12 \color{red}{-} (-1-2x) \\\Leftrightarrow & -3x+12& = &12+1+2x \\\Leftrightarrow & -3x \color{red}{+12} & = &13 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{+12} \color{blue}{-12} \color{blue}{-2x} & = &13 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-12} \\\Leftrightarrow & -3x-2x& = &13-12 \\\Leftrightarrow & -5x& = &1 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{1}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x-1)& = & -5 \color{red}{-} (6+x) \\\Leftrightarrow & -36x-6& = &-5-6-x \\\Leftrightarrow & -36x \color{red}{-6} & = &-11 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -36x+x& = &-11+6 \\\Leftrightarrow & -35x& = &-5 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-5}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+3)& = & -11 \color{red}{+} (2+x) \\\Leftrightarrow & -5x+15& = &-11+2+x \\\Leftrightarrow & -5x \color{red}{+15} & = &-9 \color{red}{+x} \\\Leftrightarrow & -5x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -5x-x& = &-9-15 \\\Leftrightarrow & -6x& = &-24 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = &\frac{-24}{ \color{red}{-6} } \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-2x-2)& = & 14 \color{red}{+} (15-3x) \\\Leftrightarrow & -4x-4& = &14+15-3x \\\Leftrightarrow & -4x \color{red}{-4} & = &29 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &29 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -4x+3x& = &29+4 \\\Leftrightarrow & -x& = &33 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{33}{ \color{red}{-1} } \\\Leftrightarrow & x = -33 & & \\ & V = \left\{ -33 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (3x-1)& = & -4 \color{red}{+} (10-2x) \\\Leftrightarrow & 15x-5& = &-4+10-2x \\\Leftrightarrow & 15x \color{red}{-5} & = &6 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{-5} \color{blue}{+5} \color{blue}{+2x} & = &6 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+5} \\\Leftrightarrow & 15x+2x& = &6+5 \\\Leftrightarrow & 17x& = &11 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{11}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{11}{17} & & \\ & V = \left\{ \frac{11}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-3x+3)& = & 15 \color{red}{-} (-11-5x) \\\Leftrightarrow & -6x+6& = &15+11+5x \\\Leftrightarrow & -6x \color{red}{+6} & = &26 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &26 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -6x-5x& = &26-6 \\\Leftrightarrow & -11x& = &20 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{20}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-5x+6)& = & 13 \color{red}{-} (-1+x) \\\Leftrightarrow & -30x+36& = &13+1-x \\\Leftrightarrow & -30x \color{red}{+36} & = &14 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -30x+x& = &14-36 \\\Leftrightarrow & -29x& = &-22 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-22}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{22}{29} & & \\ & V = \left\{ \frac{22}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (2x-3)& = & -3 \color{red}{-} (-11+x) \\\Leftrightarrow & 12x-18& = &-3+11-x \\\Leftrightarrow & 12x \color{red}{-18} & = &8 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &8+18 \\\Leftrightarrow & 13x& = &26 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{26}{ \color{red}{13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)