Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+1)& = & 5 \color{red}{+} (6+x) \\\Leftrightarrow & 4x+2& = &5+6+x \\\Leftrightarrow & 4x \color{red}{+2} & = &11 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+2} \color{blue}{-2} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-2} \\\Leftrightarrow & 4x-x& = &11-2 \\\Leftrightarrow & 3x& = &9 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{9}{ \color{red}{3} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-3x-7)& = & 1 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x-28& = &1-3+x \\\Leftrightarrow & -12x \color{red}{-28} & = &-2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -12x-x& = &-2+28 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (x+6)& = & 5 \color{red}{-} (3-2x) \\\Leftrightarrow & 3x+18& = &5-3+2x \\\Leftrightarrow & 3x \color{red}{+18} & = &2 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-18} \\\Leftrightarrow & 3x-2x& = &2-18 \\\Leftrightarrow & x& = &-16 \\ & V = \left\{ -16 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x+5)& = & -15 \color{red}{-} (-7+x) \\\Leftrightarrow & 24x+20& = &-15+7-x \\\Leftrightarrow & 24x \color{red}{+20} & = &-8 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 24x+x& = &-8-20 \\\Leftrightarrow & 25x& = &-28 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-28}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-28}{25} & & \\ & V = \left\{ \frac{-28}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-1)& = & -4 \color{red}{-} (14+3x) \\\Leftrightarrow & -8x-4& = &-4-14-3x \\\Leftrightarrow & -8x \color{red}{-4} & = &-18 \color{red}{-3x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &-18 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & -8x+3x& = &-18+4 \\\Leftrightarrow & -5x& = &-14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-6x+6)& = & 13 \color{red}{-} (4-5x) \\\Leftrightarrow & -18x+18& = &13-4+5x \\\Leftrightarrow & -18x \color{red}{+18} & = &9 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & -18x-5x& = &9-18 \\\Leftrightarrow & -23x& = &-9 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-9}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{9}{23} & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-1)& = & -7 \color{red}{-} (-15-5x) \\\Leftrightarrow & 18x-6& = &-7+15+5x \\\Leftrightarrow & 18x \color{red}{-6} & = &8 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & 18x-5x& = &8+6 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x-3)& = & -7 \color{red}{+} (5+x) \\\Leftrightarrow & 24x-18& = &-7+5+x \\\Leftrightarrow & 24x \color{red}{-18} & = &-2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 24x-x& = &-2+18 \\\Leftrightarrow & 23x& = &16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-5)& = & -2 \color{red}{+} (7+x) \\\Leftrightarrow & 12x-30& = &-2+7+x \\\Leftrightarrow & 12x \color{red}{-30} & = &5 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 12x-x& = &5+30 \\\Leftrightarrow & 11x& = &35 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{35}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{35}{11} & & \\ & V = \left\{ \frac{35}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (4x+7)& = & 8 \color{red}{+} (-5+x) \\\Leftrightarrow & 20x+35& = &8-5+x \\\Leftrightarrow & 20x \color{red}{+35} & = &3 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 20x-x& = &3-35 \\\Leftrightarrow & 19x& = &-32 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-32}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-32}{19} & & \\ & V = \left\{ \frac{-32}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x+7)& = & 2 \color{red}{+} (-8+x) \\\Leftrightarrow & 24x+42& = &2-8+x \\\Leftrightarrow & 24x \color{red}{+42} & = &-6 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 24x-x& = &-6-42 \\\Leftrightarrow & 23x& = &-48 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-48}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-48}{23} & & \\ & V = \left\{ \frac{-48}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x+3)& = & -5 \color{red}{+} (-7+3x) \\\Leftrightarrow & -4x+12& = &-5-7+3x \\\Leftrightarrow & -4x \color{red}{+12} & = &-12 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -4x-3x& = &-12-12 \\\Leftrightarrow & -7x& = &-24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{24}{7} & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)