Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x-2)& = & 14 \color{red}{+} (-2+3x) \\\Leftrightarrow & 4x-8& = &14-2+3x \\\Leftrightarrow & 4x \color{red}{-8} & = &12 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &12 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 4x-3x& = &12+8 \\\Leftrightarrow & x& = &20 \\ & V = \left\{ 20 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (6x-7)& = & 13 \color{red}{-} (-1+x) \\\Leftrightarrow & 12x-14& = &13+1-x \\\Leftrightarrow & 12x \color{red}{-14} & = &14 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & 12x+x& = &14+14 \\\Leftrightarrow & 13x& = &28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+4)& = & -3 \color{red}{+} (-1+x) \\\Leftrightarrow & -20x+16& = &-3-1+x \\\Leftrightarrow & -20x \color{red}{+16} & = &-4 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -20x-x& = &-4-16 \\\Leftrightarrow & -21x& = &-20 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-20}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x-1)& = & -11 \color{red}{-} (10+x) \\\Leftrightarrow & 12x-3& = &-11-10-x \\\Leftrightarrow & 12x \color{red}{-3} & = &-21 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-21 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &-21+3 \\\Leftrightarrow & 13x& = &-18 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-18}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-18}{13} & & \\ & V = \left\{ \frac{-18}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x+3)& = & -14 \color{red}{+} (12+x) \\\Leftrightarrow & -25x+15& = &-14+12+x \\\Leftrightarrow & -25x \color{red}{+15} & = &-2 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -25x-x& = &-2-15 \\\Leftrightarrow & -26x& = &-17 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-17}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{17}{26} & & \\ & V = \left\{ \frac{17}{26} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-4)& = & 6 \color{red}{-} (6-5x) \\\Leftrightarrow & 18x-24& = &6-6+5x \\\Leftrightarrow & 18x \color{red}{-24} & = &0 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &0 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 18x-5x& = &0+24 \\\Leftrightarrow & 13x& = &24 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{24}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{24}{13} & & \\ & V = \left\{ \frac{24}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-2)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -8x-4& = &3-14-x \\\Leftrightarrow & -8x \color{red}{-4} & = &-11 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -8x+x& = &-11+4 \\\Leftrightarrow & -7x& = &-7 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-7}{ \color{red}{-7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-6)& = & -2 \color{red}{-} (13-5x) \\\Leftrightarrow & -3x-18& = &-2-13+5x \\\Leftrightarrow & -3x \color{red}{-18} & = &-15 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-15 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & -3x-5x& = &-15+18 \\\Leftrightarrow & -8x& = &3 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{3}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-3}{8} & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-3x+1)& = & -11 \color{red}{+} (-11-5x) \\\Leftrightarrow & -18x+6& = &-11-11-5x \\\Leftrightarrow & -18x \color{red}{+6} & = &-22 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &-22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -18x+5x& = &-22-6 \\\Leftrightarrow & -13x& = &-28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-6x+2)& = & 3 \color{red}{-} (14+x) \\\Leftrightarrow & -36x+12& = &3-14-x \\\Leftrightarrow & -36x \color{red}{+12} & = &-11 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -36x+x& = &-11-12 \\\Leftrightarrow & -35x& = &-23 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-23}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{23}{35} & & \\ & V = \left\{ \frac{23}{35} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-6x-5)& = & 5 \color{red}{+} (7-5x) \\\Leftrightarrow & -36x-30& = &5+7-5x \\\Leftrightarrow & -36x \color{red}{-30} & = &12 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -36x+5x& = &12+30 \\\Leftrightarrow & -31x& = &42 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{42}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-42}{31} & & \\ & V = \left\{ \frac{-42}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x+4)& = & -9 \color{red}{+} (-15+x) \\\Leftrightarrow & 24x+24& = &-9-15+x \\\Leftrightarrow & 24x \color{red}{+24} & = &-24 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 24x-x& = &-24-24 \\\Leftrightarrow & 23x& = &-48 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-48}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-48}{23} & & \\ & V = \left\{ \frac{-48}{23} \right\} & \\\end{align}\)