Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x+7)& = & -11 \color{red}{+} (8-5x) \\\Leftrightarrow & -6x+21& = &-11+8-5x \\\Leftrightarrow & -6x \color{red}{+21} & = &-3 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & -6x+5x& = &-3-21 \\\Leftrightarrow & -x& = &-24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-24}{ \color{red}{-1} } \\\Leftrightarrow & x = 24 & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (4x-2)& = & -8 \color{red}{+} (-4+x) \\\Leftrightarrow & 16x-8& = &-8-4+x \\\Leftrightarrow & 16x \color{red}{-8} & = &-12 \color{red}{+x} \\\Leftrightarrow & 16x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 16x-x& = &-12+8 \\\Leftrightarrow & 15x& = &-4 \\\Leftrightarrow & \frac{15x}{ \color{red}{15} }& = &\frac{-4}{ \color{red}{15} } \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-2x+5)& = & 12 \color{red}{-} (15+x) \\\Leftrightarrow & -8x+20& = &12-15-x \\\Leftrightarrow & -8x \color{red}{+20} & = &-3 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -8x+x& = &-3-20 \\\Leftrightarrow & -7x& = &-23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x+4)& = & -11 \color{red}{-} (14-5x) \\\Leftrightarrow & -36x+24& = &-11-14+5x \\\Leftrightarrow & -36x \color{red}{+24} & = &-25 \color{red}{+5x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-25 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & -36x-5x& = &-25-24 \\\Leftrightarrow & -41x& = &-49 \\\Leftrightarrow & \frac{-41x}{ \color{red}{-41} }& = &\frac{-49}{ \color{red}{-41} } \\\Leftrightarrow & x = \frac{49}{41} & & \\ & V = \left\{ \frac{49}{41} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-5x-5)& = & 1 \color{red}{+} (6+3x) \\\Leftrightarrow & -20x-20& = &1+6+3x \\\Leftrightarrow & -20x \color{red}{-20} & = &7 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -20x-3x& = &7+20 \\\Leftrightarrow & -23x& = &27 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{27}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-27}{23} & & \\ & V = \left\{ \frac{-27}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (6x-2)& = & 7 \color{red}{+} (4+x) \\\Leftrightarrow & 24x-8& = &7+4+x \\\Leftrightarrow & 24x \color{red}{-8} & = &11 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 24x-x& = &11+8 \\\Leftrightarrow & 23x& = &19 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{19}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+4)& = & 13 \color{red}{+} (7+4x) \\\Leftrightarrow & 3x+12& = &13+7+4x \\\Leftrightarrow & 3x \color{red}{+12} & = &20 \color{red}{+4x} \\\Leftrightarrow & 3x \color{red}{+12} \color{blue}{-12} \color{blue}{-4x} & = &20 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-12} \\\Leftrightarrow & 3x-4x& = &20-12 \\\Leftrightarrow & -x& = &8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{8}{ \color{red}{-1} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x-1)& = & 13 \color{red}{+} (14+x) \\\Leftrightarrow & -20x-5& = &13+14+x \\\Leftrightarrow & -20x \color{red}{-5} & = &27 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &27 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & -20x-x& = &27+5 \\\Leftrightarrow & -21x& = &32 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{32}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-32}{21} & & \\ & V = \left\{ \frac{-32}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+7)& = & -6 \color{red}{+} (-9+4x) \\\Leftrightarrow & 15x+21& = &-6-9+4x \\\Leftrightarrow & 15x \color{red}{+21} & = &-15 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-4x} & = &-15 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-21} \\\Leftrightarrow & 15x-4x& = &-15-21 \\\Leftrightarrow & 11x& = &-36 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-36}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-36}{11} & & \\ & V = \left\{ \frac{-36}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (x-6)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & 6x-36& = &8-4+x \\\Leftrightarrow & 6x \color{red}{-36} & = &4 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 6x-x& = &4+36 \\\Leftrightarrow & 5x& = &40 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{40}{ \color{red}{5} } \\\Leftrightarrow & x = 8 & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (2x+7)& = & -5 \color{red}{+} (5+3x) \\\Leftrightarrow & 10x+35& = &-5+5+3x \\\Leftrightarrow & 10x \color{red}{+35} & = &0 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+35} \color{blue}{-35} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-35} \\\Leftrightarrow & 10x-3x& = &0-35 \\\Leftrightarrow & 7x& = &-35 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-35}{ \color{red}{7} } \\\Leftrightarrow & x = -5 & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x+7)& = & 5 \color{red}{+} (11+x) \\\Leftrightarrow & 30x+35& = &5+11+x \\\Leftrightarrow & 30x \color{red}{+35} & = &16 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 30x-x& = &16-35 \\\Leftrightarrow & 29x& = &-19 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-19}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-19}{29} & & \\ & V = \left\{ \frac{-19}{29} \right\} & \\\end{align}\)