Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x-4)& = & 2 \color{red}{-} (2-3x) \\\Leftrightarrow & -10x-20& = &2-2+3x \\\Leftrightarrow & -10x \color{red}{-20} & = &0 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -10x-3x& = &0+20 \\\Leftrightarrow & -13x& = &20 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{20}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x-2)& = & -5 \color{red}{-} (8+x) \\\Leftrightarrow & -20x-10& = &-5-8-x \\\Leftrightarrow & -20x \color{red}{-10} & = &-13 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & -20x+x& = &-13+10 \\\Leftrightarrow & -19x& = &-3 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-3}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (6x-6)& = & -5 \color{red}{+} (9+x) \\\Leftrightarrow & 30x-30& = &-5+9+x \\\Leftrightarrow & 30x \color{red}{-30} & = &4 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &4+30 \\\Leftrightarrow & 29x& = &34 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{34}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{34}{29} & & \\ & V = \left\{ \frac{34}{29} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x-5)& = & 12 \color{red}{+} (-14+x) \\\Leftrightarrow & 2x-10& = &12-14+x \\\Leftrightarrow & 2x \color{red}{-10} & = &-2 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 2x-x& = &-2+10 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-4)& = & -10 \color{red}{-} (15-3x) \\\Leftrightarrow & 4x-16& = &-10-15+3x \\\Leftrightarrow & 4x \color{red}{-16} & = &-25 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-16} \color{blue}{+16} \color{blue}{-3x} & = &-25 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+16} \\\Leftrightarrow & 4x-3x& = &-25+16 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x+6)& = & -3 \color{red}{-} (12+4x) \\\Leftrightarrow & 25x+30& = &-3-12-4x \\\Leftrightarrow & 25x \color{red}{+30} & = &-15 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+4x} & = &-15 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-30} \\\Leftrightarrow & 25x+4x& = &-15-30 \\\Leftrightarrow & 29x& = &-45 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-45}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-45}{29} & & \\ & V = \left\{ \frac{-45}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-6x+4)& = & 6 \color{red}{+} (4+x) \\\Leftrightarrow & -36x+24& = &6+4+x \\\Leftrightarrow & -36x \color{red}{+24} & = &10 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -36x-x& = &10-24 \\\Leftrightarrow & -37x& = &-14 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{-14}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{14}{37} & & \\ & V = \left\{ \frac{14}{37} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x+6)& = & 5 \color{red}{+} (6+x) \\\Leftrightarrow & -12x+36& = &5+6+x \\\Leftrightarrow & -12x \color{red}{+36} & = &11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -12x-x& = &11-36 \\\Leftrightarrow & -13x& = &-25 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-25}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{25}{13} & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x+1)& = & 4 \color{red}{-} (-8-5x) \\\Leftrightarrow & 36x+6& = &4+8+5x \\\Leftrightarrow & 36x \color{red}{+6} & = &12 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 36x-5x& = &12-6 \\\Leftrightarrow & 31x& = &6 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{6}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (5x-6)& = & -14 \color{red}{+} (-2+x) \\\Leftrightarrow & 20x-24& = &-14-2+x \\\Leftrightarrow & 20x \color{red}{-24} & = &-16 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 20x-x& = &-16+24 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-3)& = & -8 \color{red}{+} (4+x) \\\Leftrightarrow & -6x-18& = &-8+4+x \\\Leftrightarrow & -6x \color{red}{-18} & = &-4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -6x-x& = &-4+18 \\\Leftrightarrow & -7x& = &14 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{14}{ \color{red}{-7} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x-7)& = & -13 \color{red}{+} (-13+x) \\\Leftrightarrow & -12x-21& = &-13-13+x \\\Leftrightarrow & -12x \color{red}{-21} & = &-26 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -12x-x& = &-26+21 \\\Leftrightarrow & -13x& = &-5 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-5}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)