Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (2x+3)& = & -13 \color{red}{-} (14-3x) \\\Leftrightarrow & 4x+6& = &-13-14+3x \\\Leftrightarrow & 4x \color{red}{+6} & = &-27 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+6} \color{blue}{-6} \color{blue}{-3x} & = &-27 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-6} \\\Leftrightarrow & 4x-3x& = &-27-6 \\\Leftrightarrow & x& = &-33 \\ & V = \left\{ -33 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-4x+7)& = & 7 \color{red}{-} (12+x) \\\Leftrightarrow & -12x+21& = &7-12-x \\\Leftrightarrow & -12x \color{red}{+21} & = &-5 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -12x+x& = &-5-21 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x-7)& = & -9 \color{red}{+} (6+x) \\\Leftrightarrow & -20x-28& = &-9+6+x \\\Leftrightarrow & -20x \color{red}{-28} & = &-3 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -20x-x& = &-3+28 \\\Leftrightarrow & -21x& = &25 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{25}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-25}{21} & & \\ & V = \left\{ \frac{-25}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-x+2)& = & 2 \color{red}{-} (12+4x) \\\Leftrightarrow & -5x+10& = &2-12-4x \\\Leftrightarrow & -5x \color{red}{+10} & = &-10 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &-10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & -5x+4x& = &-10-10 \\\Leftrightarrow & -x& = &-20 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-20}{ \color{red}{-1} } \\\Leftrightarrow & x = 20 & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (4x-1)& = & -6 \color{red}{-} (3+x) \\\Leftrightarrow & 12x-3& = &-6-3-x \\\Leftrightarrow & 12x \color{red}{-3} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 12x+x& = &-9+3 \\\Leftrightarrow & 13x& = &-6 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-6}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-6}{13} & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+7)& = & -10 \color{red}{+} (-3+x) \\\Leftrightarrow & 24x+42& = &-10-3+x \\\Leftrightarrow & 24x \color{red}{+42} & = &-13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 24x-x& = &-13-42 \\\Leftrightarrow & 23x& = &-55 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-55}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-55}{23} & & \\ & V = \left\{ \frac{-55}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (x+5)& = & -5 \color{red}{-} (1-2x) \\\Leftrightarrow & 5x+25& = &-5-1+2x \\\Leftrightarrow & 5x \color{red}{+25} & = &-6 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{+25} \color{blue}{-25} \color{blue}{-2x} & = &-6 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-25} \\\Leftrightarrow & 5x-2x& = &-6-25 \\\Leftrightarrow & 3x& = &-31 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-31}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-31}{3} & & \\ & V = \left\{ \frac{-31}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-x-4)& = & 3 \color{red}{+} (3+x) \\\Leftrightarrow & -4x-16& = &3+3+x \\\Leftrightarrow & -4x \color{red}{-16} & = &6 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -4x-x& = &6+16 \\\Leftrightarrow & -5x& = &22 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{22}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-22}{5} & & \\ & V = \left\{ \frac{-22}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (2x-6)& = & -14 \color{red}{-} (-15+x) \\\Leftrightarrow & 4x-12& = &-14+15-x \\\Leftrightarrow & 4x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 4x+x& = &1+12 \\\Leftrightarrow & 5x& = &13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x+2)& = & -3 \color{red}{-} (13-5x) \\\Leftrightarrow & -6x+12& = &-3-13+5x \\\Leftrightarrow & -6x \color{red}{+12} & = &-16 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & -6x-5x& = &-16-12 \\\Leftrightarrow & -11x& = &-28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x+4)& = & -12 \color{red}{+} (1+x) \\\Leftrightarrow & 20x+16& = &-12+1+x \\\Leftrightarrow & 20x \color{red}{+16} & = &-11 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & 20x-x& = &-11-16 \\\Leftrightarrow & 19x& = &-27 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-27}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-27}{19} & & \\ & V = \left\{ \frac{-27}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x-1)& = & -14 \color{red}{+} (6+x) \\\Leftrightarrow & 18x-6& = &-14+6+x \\\Leftrightarrow & 18x \color{red}{-6} & = &-8 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &-8+6 \\\Leftrightarrow & 17x& = &-2 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-2}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)