Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x-1)& = & -3 \color{red}{-} (12-2x) \\\Leftrightarrow & 5x-5& = &-3-12+2x \\\Leftrightarrow & 5x \color{red}{-5} & = &-15 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{-2x} & = &-15 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+5} \\\Leftrightarrow & 5x-2x& = &-15+5 \\\Leftrightarrow & 3x& = &-10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x+7)& = & -12 \color{red}{-} (-3+x) \\\Leftrightarrow & 20x+28& = &-12+3-x \\\Leftrightarrow & 20x \color{red}{+28} & = &-9 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 20x+x& = &-9-28 \\\Leftrightarrow & 21x& = &-37 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{-37}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{-37}{21} & & \\ & V = \left\{ \frac{-37}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x-5)& = & -1 \color{red}{+} (3-5x) \\\Leftrightarrow & 18x-15& = &-1+3-5x \\\Leftrightarrow & 18x \color{red}{-15} & = &2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 18x+5x& = &2+15 \\\Leftrightarrow & 23x& = &17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{17}{23} & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-7)& = & -3 \color{red}{-} (-3+x) \\\Leftrightarrow & 15x-35& = &-3+3-x \\\Leftrightarrow & 15x \color{red}{-35} & = &0 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 15x+x& = &0+35 \\\Leftrightarrow & 16x& = &35 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{35}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{35}{16} & & \\ & V = \left\{ \frac{35}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-6)& = & -8 \color{red}{+} (-4+2x) \\\Leftrightarrow & 3x-18& = &-8-4+2x \\\Leftrightarrow & 3x \color{red}{-18} & = &-12 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &-12 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & 3x-2x& = &-12+18 \\\Leftrightarrow & x& = &6 \\ & V = \left\{ 6 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-x+4)& = & -11 \color{red}{-} (2+x) \\\Leftrightarrow & -5x+20& = &-11-2-x \\\Leftrightarrow & -5x \color{red}{+20} & = &-13 \color{red}{-x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -5x+x& = &-13-20 \\\Leftrightarrow & -4x& = &-33 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-33}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{33}{4} & & \\ & V = \left\{ \frac{33}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-x+1)& = & 15 \color{red}{-} (9+4x) \\\Leftrightarrow & -3x+3& = &15-9-4x \\\Leftrightarrow & -3x \color{red}{+3} & = &6 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{+3} \color{blue}{-3} \color{blue}{+4x} & = &6 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-3} \\\Leftrightarrow & -3x+4x& = &6-3 \\\Leftrightarrow & x& = &3 \\ & V = \left\{ 3 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x+4)& = & 15 \color{red}{-} (-9+x) \\\Leftrightarrow & 4x+8& = &15+9-x \\\Leftrightarrow & 4x \color{red}{+8} & = &24 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 4x+x& = &24-8 \\\Leftrightarrow & 5x& = &16 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{16}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-4x+5)& = & -11 \color{red}{+} (-15+x) \\\Leftrightarrow & -20x+25& = &-11-15+x \\\Leftrightarrow & -20x \color{red}{+25} & = &-26 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -20x-x& = &-26-25 \\\Leftrightarrow & -21x& = &-51 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-51}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x+5)& = & 6 \color{red}{-} (-14+x) \\\Leftrightarrow & 6x+30& = &6+14-x \\\Leftrightarrow & 6x \color{red}{+30} & = &20 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 6x+x& = &20-30 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-6x-2)& = & -6 \color{red}{+} (2-5x) \\\Leftrightarrow & -18x-6& = &-6+2-5x \\\Leftrightarrow & -18x \color{red}{-6} & = &-4 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -18x+5x& = &-4+6 \\\Leftrightarrow & -13x& = &2 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{2}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-x-3)& = & 11 \color{red}{+} (-6+2x) \\\Leftrightarrow & -3x-9& = &11-6+2x \\\Leftrightarrow & -3x \color{red}{-9} & = &5 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-9} \color{blue}{+9} \color{blue}{-2x} & = &5 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+9} \\\Leftrightarrow & -3x-2x& = &5+9 \\\Leftrightarrow & -5x& = &14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)