Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x-1)& = & -12 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x-6& = &-12-6+x \\\Leftrightarrow & -30x \color{red}{-6} & = &-18 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -30x-x& = &-18+6 \\\Leftrightarrow & -31x& = &-12 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-12}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{12}{31} & & \\ & V = \left\{ \frac{12}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-x-2)& = & 5 \color{red}{-} (-15+x) \\\Leftrightarrow & -2x-4& = &5+15-x \\\Leftrightarrow & -2x \color{red}{-4} & = &20 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -2x+x& = &20+4 \\\Leftrightarrow & -x& = &24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{24}{ \color{red}{-1} } \\\Leftrightarrow & x = -24 & & \\ & V = \left\{ -24 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x-4)& = & 9 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-20& = &9+14-x \\\Leftrightarrow & 30x \color{red}{-20} & = &23 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 30x+x& = &23+20 \\\Leftrightarrow & 31x& = &43 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{43}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{43}{31} & & \\ & V = \left\{ \frac{43}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x-4)& = & -14 \color{red}{+} (7+x) \\\Leftrightarrow & -30x-20& = &-14+7+x \\\Leftrightarrow & -30x \color{red}{-20} & = &-7 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & -30x-x& = &-7+20 \\\Leftrightarrow & -31x& = &13 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{13}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-13}{31} & & \\ & V = \left\{ \frac{-13}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (x-4)& = & 6 \color{red}{-} (7+x) \\\Leftrightarrow & 5x-20& = &6-7-x \\\Leftrightarrow & 5x \color{red}{-20} & = &-1 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 5x+x& = &-1+20 \\\Leftrightarrow & 6x& = &19 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{19}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{19}{6} & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-1)& = & -4 \color{red}{-} (-11+x) \\\Leftrightarrow & -6x-6& = &-4+11-x \\\Leftrightarrow & -6x \color{red}{-6} & = &7 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -6x+x& = &7+6 \\\Leftrightarrow & -5x& = &13 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{13}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x+1)& = & 3 \color{red}{-} (2+x) \\\Leftrightarrow & 24x+6& = &3-2-x \\\Leftrightarrow & 24x \color{red}{+6} & = &1 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 24x+x& = &1-6 \\\Leftrightarrow & 25x& = &-5 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-5}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x-4)& = & 8 \color{red}{+} (-3+x) \\\Leftrightarrow & 30x-24& = &8-3+x \\\Leftrightarrow & 30x \color{red}{-24} & = &5 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 30x-x& = &5+24 \\\Leftrightarrow & 29x& = &29 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{29}{ \color{red}{29} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+2)& = & 6 \color{red}{+} (-6+x) \\\Leftrightarrow & -20x+10& = &6-6+x \\\Leftrightarrow & -20x \color{red}{+10} & = &0 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -20x-x& = &0-10 \\\Leftrightarrow & -21x& = &-10 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-10}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x+7)& = & 15 \color{red}{-} (-15-5x) \\\Leftrightarrow & -8x+28& = &15+15+5x \\\Leftrightarrow & -8x \color{red}{+28} & = &30 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{+28} \color{blue}{-28} \color{blue}{-5x} & = &30 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-28} \\\Leftrightarrow & -8x-5x& = &30-28 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+6)& = & 9 \color{red}{-} (-14+x) \\\Leftrightarrow & 20x+24& = &9+14-x \\\Leftrightarrow & 20x \color{red}{+24} & = &23 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 20x+x& = &23-24 \\\Leftrightarrow & 21x& = &-1 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-1}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-1}{21} & & \\ & V = \left\{ \frac{-1}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-5x+2)& = & -4 \color{red}{+} (6+x) \\\Leftrightarrow & -10x+4& = &-4+6+x \\\Leftrightarrow & -10x \color{red}{+4} & = &2 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -10x-x& = &2-4 \\\Leftrightarrow & -11x& = &-2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)