Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+1)& = & -3 \color{red}{-} (9-3x) \\\Leftrightarrow & 25x+5& = &-3-9+3x \\\Leftrightarrow & 25x \color{red}{+5} & = &-12 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{+5} \color{blue}{-5} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-5} \\\Leftrightarrow & 25x-3x& = &-12-5 \\\Leftrightarrow & 22x& = &-17 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{-17}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{-17}{22} & & \\ & V = \left\{ \frac{-17}{22} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-x-1)& = & -11 \color{red}{-} (-15-4x) \\\Leftrightarrow & -5x-5& = &-11+15+4x \\\Leftrightarrow & -5x \color{red}{-5} & = &4 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -5x-4x& = &4+5 \\\Leftrightarrow & -9x& = &9 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{9}{ \color{red}{-9} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-2x-3)& = & 14 \color{red}{+} (10+x) \\\Leftrightarrow & -12x-18& = &14+10+x \\\Leftrightarrow & -12x \color{red}{-18} & = &24 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &24+18 \\\Leftrightarrow & -13x& = &42 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{42}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-42}{13} & & \\ & V = \left\{ \frac{-42}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-1)& = & -6 \color{red}{-} (-14+x) \\\Leftrightarrow & -6x-6& = &-6+14-x \\\Leftrightarrow & -6x \color{red}{-6} & = &8 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &8+6 \\\Leftrightarrow & -5x& = &14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (6x+2)& = & 13 \color{red}{-} (1+x) \\\Leftrightarrow & 30x+10& = &13-1-x \\\Leftrightarrow & 30x \color{red}{+10} & = &12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 30x+x& = &12-10 \\\Leftrightarrow & 31x& = &2 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{2}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{2}{31} & & \\ & V = \left\{ \frac{2}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x+1)& = & 10 \color{red}{-} (10+x) \\\Leftrightarrow & 6x+2& = &10-10-x \\\Leftrightarrow & 6x \color{red}{+2} & = &0 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & 6x+x& = &0-2 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x-7)& = & -2 \color{red}{+} (7+x) \\\Leftrightarrow & -10x-14& = &-2+7+x \\\Leftrightarrow & -10x \color{red}{-14} & = &5 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -10x-x& = &5+14 \\\Leftrightarrow & -11x& = &19 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{19}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-2)& = & -13 \color{red}{+} (-3+x) \\\Leftrightarrow & -6x-12& = &-13-3+x \\\Leftrightarrow & -6x \color{red}{-12} & = &-16 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -6x-x& = &-16+12 \\\Leftrightarrow & -7x& = &-4 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-4}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-6x-6)& = & 13 \color{red}{+} (4+x) \\\Leftrightarrow & -12x-12& = &13+4+x \\\Leftrightarrow & -12x \color{red}{-12} & = &17 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &17+12 \\\Leftrightarrow & -13x& = &29 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{29}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x-4)& = & -14 \color{red}{+} (-14-3x) \\\Leftrightarrow & 4x-8& = &-14-14-3x \\\Leftrightarrow & 4x \color{red}{-8} & = &-28 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &-28 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 4x+3x& = &-28+8 \\\Leftrightarrow & 7x& = &-20 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-20}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x-1)& = & 15 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x-6& = &15-15+x \\\Leftrightarrow & 30x \color{red}{-6} & = &0 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 30x-x& = &0+6 \\\Leftrightarrow & 29x& = &6 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{6}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{6}{29} & & \\ & V = \left\{ \frac{6}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+3)& = & -10 \color{red}{+} (6+x) \\\Leftrightarrow & 24x+12& = &-10+6+x \\\Leftrightarrow & 24x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 24x-x& = &-4-12 \\\Leftrightarrow & 23x& = &-16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-16}{23} & & \\ & V = \left\{ \frac{-16}{23} \right\} & \\\end{align}\)