Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+6)& = & 10 \color{red}{-} (-8+x) \\\Leftrightarrow & 10x+12& = &10+8-x \\\Leftrightarrow & 10x \color{red}{+12} & = &18 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 10x+x& = &18-12 \\\Leftrightarrow & 11x& = &6 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{6}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (4x+1)& = & -11 \color{red}{+} (-7+x) \\\Leftrightarrow & 12x+3& = &-11-7+x \\\Leftrightarrow & 12x \color{red}{+3} & = &-18 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+3} \color{blue}{-3} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-3} \\\Leftrightarrow & 12x-x& = &-18-3 \\\Leftrightarrow & 11x& = &-21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-21}{11} & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (5x+1)& = & 5 \color{red}{-} (-1+x) \\\Leftrightarrow & 20x+4& = &5+1-x \\\Leftrightarrow & 20x \color{red}{+4} & = &6 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 20x+x& = &6-4 \\\Leftrightarrow & 21x& = &2 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{2}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-3x+3)& = & -5 \color{red}{-} (15+x) \\\Leftrightarrow & -6x+6& = &-5-15-x \\\Leftrightarrow & -6x \color{red}{+6} & = &-20 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -6x+x& = &-20-6 \\\Leftrightarrow & -5x& = &-26 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-26}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{26}{5} & & \\ & V = \left\{ \frac{26}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-x-4)& = & 6 \color{red}{-} (6+x) \\\Leftrightarrow & -6x-24& = &6-6-x \\\Leftrightarrow & -6x \color{red}{-24} & = &0 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -6x+x& = &0+24 \\\Leftrightarrow & -5x& = &24 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{24}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-24}{5} & & \\ & V = \left\{ \frac{-24}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-6x+7)& = & -12 \color{red}{+} (-5-5x) \\\Leftrightarrow & -36x+42& = &-12-5-5x \\\Leftrightarrow & -36x \color{red}{+42} & = &-17 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-17 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -36x+5x& = &-17-42 \\\Leftrightarrow & -31x& = &-59 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-59}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{59}{31} & & \\ & V = \left\{ \frac{59}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (5x+7)& = & 5 \color{red}{-} (6-2x) \\\Leftrightarrow & 15x+21& = &5-6+2x \\\Leftrightarrow & 15x \color{red}{+21} & = &-1 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & 15x-2x& = &-1-21 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (4x+6)& = & 15 \color{red}{+} (-1+x) \\\Leftrightarrow & 20x+30& = &15-1+x \\\Leftrightarrow & 20x \color{red}{+30} & = &14 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 20x-x& = &14-30 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (x+6)& = & -10 \color{red}{+} (-6+x) \\\Leftrightarrow & 4x+24& = &-10-6+x \\\Leftrightarrow & 4x \color{red}{+24} & = &-16 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 4x-x& = &-16-24 \\\Leftrightarrow & 3x& = &-40 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-40}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-40}{3} & & \\ & V = \left\{ \frac{-40}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-2x-2)& = & 10 \color{red}{+} (1+x) \\\Leftrightarrow & -6x-6& = &10+1+x \\\Leftrightarrow & -6x \color{red}{-6} & = &11 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &11+6 \\\Leftrightarrow & -7x& = &17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-2x-1)& = & -11 \color{red}{+} (4-3x) \\\Leftrightarrow & -10x-5& = &-11+4-3x \\\Leftrightarrow & -10x \color{red}{-5} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & -10x+3x& = &-7+5 \\\Leftrightarrow & -7x& = &-2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (3x+1)& = & -2 \color{red}{-} (7-2x) \\\Leftrightarrow & 15x+5& = &-2-7+2x \\\Leftrightarrow & 15x \color{red}{+5} & = &-9 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &-9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & 15x-2x& = &-9-5 \\\Leftrightarrow & 13x& = &-14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-14}{13} & & \\ & V = \left\{ \frac{-14}{13} \right\} & \\\end{align}\)