Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x-1)& = & 15 \color{red}{+} (-6+x) \\\Leftrightarrow & -30x-5& = &15-6+x \\\Leftrightarrow & -30x \color{red}{-5} & = &9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -30x-x& = &9+5 \\\Leftrightarrow & -31x& = &14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-14}{31} & & \\ & V = \left\{ \frac{-14}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-3x-3)& = & 2 \color{red}{+} (2-5x) \\\Leftrightarrow & -18x-18& = &2+2-5x \\\Leftrightarrow & -18x \color{red}{-18} & = &4 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+18} \\\Leftrightarrow & -18x+5x& = &4+18 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x+5)& = & 6 \color{red}{+} (3-5x) \\\Leftrightarrow & 6x+30& = &6+3-5x \\\Leftrightarrow & 6x \color{red}{+30} & = &9 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & 6x+5x& = &9-30 \\\Leftrightarrow & 11x& = &-21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-7)& = & 9 \color{red}{-} (2+x) \\\Leftrightarrow & 20x-35& = &9-2-x \\\Leftrightarrow & 20x \color{red}{-35} & = &7 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 20x+x& = &7+35 \\\Leftrightarrow & 21x& = &42 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{42}{ \color{red}{21} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x-7)& = & -8 \color{red}{+} (8+x) \\\Leftrightarrow & 6x-21& = &-8+8+x \\\Leftrightarrow & 6x \color{red}{-21} & = &0 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 6x-x& = &0+21 \\\Leftrightarrow & 5x& = &21 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{21}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{21}{5} & & \\ & V = \left\{ \frac{21}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x+5)& = & -4 \color{red}{+} (-4+x) \\\Leftrightarrow & 10x+25& = &-4-4+x \\\Leftrightarrow & 10x \color{red}{+25} & = &-8 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 10x-x& = &-8-25 \\\Leftrightarrow & 9x& = &-33 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-33}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-11}{3} & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x+6)& = & -12 \color{red}{-} (-9+x) \\\Leftrightarrow & -36x+36& = &-12+9-x \\\Leftrightarrow & -36x \color{red}{+36} & = &-3 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -36x+x& = &-3-36 \\\Leftrightarrow & -35x& = &-39 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-39}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{39}{35} & & \\ & V = \left\{ \frac{39}{35} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x+2)& = & -14 \color{red}{-} (-13+x) \\\Leftrightarrow & 30x+12& = &-14+13-x \\\Leftrightarrow & 30x \color{red}{+12} & = &-1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 30x+x& = &-1-12 \\\Leftrightarrow & 31x& = &-13 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-13}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-13}{31} & & \\ & V = \left\{ \frac{-13}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x+4)& = & -3 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x+12& = &-3-1+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-4-12 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (5x-4)& = & -10 \color{red}{-} (-13-4x) \\\Leftrightarrow & 25x-20& = &-10+13+4x \\\Leftrightarrow & 25x \color{red}{-20} & = &3 \color{red}{+4x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &3 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & 25x-4x& = &3+20 \\\Leftrightarrow & 21x& = &23 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{23}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{23}{21} & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-3x+7)& = & -12 \color{red}{+} (-9-5x) \\\Leftrightarrow & -18x+42& = &-12-9-5x \\\Leftrightarrow & -18x \color{red}{+42} & = &-21 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -18x+5x& = &-21-42 \\\Leftrightarrow & -13x& = &-63 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-63}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{63}{13} & & \\ & V = \left\{ \frac{63}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x-7)& = & 4 \color{red}{-} (-4+x) \\\Leftrightarrow & 2x-14& = &4+4-x \\\Leftrightarrow & 2x \color{red}{-14} & = &8 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 2x+x& = &8+14 \\\Leftrightarrow & 3x& = &22 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{22}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{22}{3} & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)