Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (5x+7)& = & -1 \color{red}{-} (1-2x) \\\Leftrightarrow & 15x+21& = &-1-1+2x \\\Leftrightarrow & 15x \color{red}{+21} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & 15x-2x& = &-2-21 \\\Leftrightarrow & 13x& = &-23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x-3)& = & -2 \color{red}{+} (-6+x) \\\Leftrightarrow & 6x-9& = &-2-6+x \\\Leftrightarrow & 6x \color{red}{-9} & = &-8 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & 6x-x& = &-8+9 \\\Leftrightarrow & 5x& = &1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x+3)& = & 14 \color{red}{-} (6+x) \\\Leftrightarrow & -10x+15& = &14-6-x \\\Leftrightarrow & -10x \color{red}{+15} & = &8 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & -10x+x& = &8-15 \\\Leftrightarrow & -9x& = &-7 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-7}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{7}{9} & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-x+5)& = & 7 \color{red}{+} (5+3x) \\\Leftrightarrow & -2x+10& = &7+5+3x \\\Leftrightarrow & -2x \color{red}{+10} & = &12 \color{red}{+3x} \\\Leftrightarrow & -2x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -2x-3x& = &12-10 \\\Leftrightarrow & -5x& = &2 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{2}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x+7)& = & 2 \color{red}{+} (7-5x) \\\Leftrightarrow & 36x+42& = &2+7-5x \\\Leftrightarrow & 36x \color{red}{+42} & = &9 \color{red}{-5x} \\\Leftrightarrow & 36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 36x+5x& = &9-42 \\\Leftrightarrow & 41x& = &-33 \\\Leftrightarrow & \frac{41x}{ \color{red}{41} }& = &\frac{-33}{ \color{red}{41} } \\\Leftrightarrow & x = \frac{-33}{41} & & \\ & V = \left\{ \frac{-33}{41} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x+4)& = & -3 \color{red}{-} (5+x) \\\Leftrightarrow & 16x+16& = &-3-5-x \\\Leftrightarrow & 16x \color{red}{+16} & = &-8 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 16x+x& = &-8-16 \\\Leftrightarrow & 17x& = &-24 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-24}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-24}{17} & & \\ & V = \left\{ \frac{-24}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x+1)& = & 2 \color{red}{+} (15-5x) \\\Leftrightarrow & 18x+3& = &2+15-5x \\\Leftrightarrow & 18x \color{red}{+3} & = &17 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & 18x+5x& = &17-3 \\\Leftrightarrow & 23x& = &14 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{14}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{14}{23} & & \\ & V = \left\{ \frac{14}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x+6)& = & -11 \color{red}{+} (2+x) \\\Leftrightarrow & -6x+18& = &-11+2+x \\\Leftrightarrow & -6x \color{red}{+18} & = &-9 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-9 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -6x-x& = &-9-18 \\\Leftrightarrow & -7x& = &-27 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-27}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{27}{7} & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-4x-4)& = & -7 \color{red}{+} (8+3x) \\\Leftrightarrow & -16x-16& = &-7+8+3x \\\Leftrightarrow & -16x \color{red}{-16} & = &1 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & -16x-3x& = &1+16 \\\Leftrightarrow & -19x& = &17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-17}{19} & & \\ & V = \left\{ \frac{-17}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-2x+7)& = & 4 \color{red}{-} (15+x) \\\Leftrightarrow & -12x+42& = &4-15-x \\\Leftrightarrow & -12x \color{red}{+42} & = &-11 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &-11-42 \\\Leftrightarrow & -11x& = &-53 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-53}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{53}{11} & & \\ & V = \left\{ \frac{53}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-2x-4)& = & 10 \color{red}{-} (-8-5x) \\\Leftrightarrow & -6x-12& = &10+8+5x \\\Leftrightarrow & -6x \color{red}{-12} & = &18 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &18 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -6x-5x& = &18+12 \\\Leftrightarrow & -11x& = &30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-30}{11} & & \\ & V = \left\{ \frac{-30}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (5x-7)& = & 10 \color{red}{-} (-1-2x) \\\Leftrightarrow & 15x-21& = &10+1+2x \\\Leftrightarrow & 15x \color{red}{-21} & = &11 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & 15x-2x& = &11+21 \\\Leftrightarrow & 13x& = &32 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{32}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{32}{13} & & \\ & V = \left\{ \frac{32}{13} \right\} & \\\end{align}\)