Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x+2)& = & 2 \color{red}{-} (-1+3x) \\\Leftrightarrow & -20x+10& = &2+1-3x \\\Leftrightarrow & -20x \color{red}{+10} & = &3 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &3 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -20x+3x& = &3-10 \\\Leftrightarrow & -17x& = &-7 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{-7}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{7}{17} & & \\ & V = \left\{ \frac{7}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (2x+3)& = & 6 \color{red}{-} (3+x) \\\Leftrightarrow & 12x+18& = &6-3-x \\\Leftrightarrow & 12x \color{red}{+18} & = &3 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 12x+x& = &3-18 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x+7)& = & -9 \color{red}{+} (-4+3x) \\\Leftrightarrow & -10x+35& = &-9-4+3x \\\Leftrightarrow & -10x \color{red}{+35} & = &-13 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &-13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & -10x-3x& = &-13-35 \\\Leftrightarrow & -13x& = &-48 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-48}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{48}{13} & & \\ & V = \left\{ \frac{48}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x-3)& = & -2 \color{red}{+} (14+5x) \\\Leftrightarrow & 24x-12& = &-2+14+5x \\\Leftrightarrow & 24x \color{red}{-12} & = &12 \color{red}{+5x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & 24x-5x& = &12+12 \\\Leftrightarrow & 19x& = &24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{24}{19} & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x+5)& = & 2 \color{red}{+} (8+x) \\\Leftrightarrow & 10x+25& = &2+8+x \\\Leftrightarrow & 10x \color{red}{+25} & = &10 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 10x-x& = &10-25 \\\Leftrightarrow & 9x& = &-15 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-15}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-5}{3} & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (3x-3)& = & -13 \color{red}{+} (3-5x) \\\Leftrightarrow & 6x-6& = &-13+3-5x \\\Leftrightarrow & 6x \color{red}{-6} & = &-10 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &-10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & 6x+5x& = &-10+6 \\\Leftrightarrow & 11x& = &-4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (2x+7)& = & -2 \color{red}{-} (3+5x) \\\Leftrightarrow & 12x+42& = &-2-3-5x \\\Leftrightarrow & 12x \color{red}{+42} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 12x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 12x+5x& = &-5-42 \\\Leftrightarrow & 17x& = &-47 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-47}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-47}{17} & & \\ & V = \left\{ \frac{-47}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x-2)& = & -14 \color{red}{-} (-14+x) \\\Leftrightarrow & 20x-10& = &-14+14-x \\\Leftrightarrow & 20x \color{red}{-10} & = &0 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 20x+x& = &0+10 \\\Leftrightarrow & 21x& = &10 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{10}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-6x+5)& = & 8 \color{red}{+} (-7+x) \\\Leftrightarrow & -24x+20& = &8-7+x \\\Leftrightarrow & -24x \color{red}{+20} & = &1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -24x-x& = &1-20 \\\Leftrightarrow & -25x& = &-19 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-19}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{19}{25} & & \\ & V = \left\{ \frac{19}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+6)& = & 14 \color{red}{+} (-10+4x) \\\Leftrightarrow & 15x+18& = &14-10+4x \\\Leftrightarrow & 15x \color{red}{+18} & = &4 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &4 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & 15x-4x& = &4-18 \\\Leftrightarrow & 11x& = &-14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x+6)& = & -11 \color{red}{-} (-12+5x) \\\Leftrightarrow & 6x+36& = &-11+12-5x \\\Leftrightarrow & 6x \color{red}{+36} & = &1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & 6x+5x& = &1-36 \\\Leftrightarrow & 11x& = &-35 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-35}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-35}{11} & & \\ & V = \left\{ \frac{-35}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x+5)& = & -3 \color{red}{-} (-12+x) \\\Leftrightarrow & 30x+30& = &-3+12-x \\\Leftrightarrow & 30x \color{red}{+30} & = &9 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 30x+x& = &9-30 \\\Leftrightarrow & 31x& = &-21 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-21}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-21}{31} & & \\ & V = \left\{ \frac{-21}{31} \right\} & \\\end{align}\)