Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-7)& = & -7 \color{red}{+} (14+x) \\\Leftrightarrow & -18x-21& = &-7+14+x \\\Leftrightarrow & -18x \color{red}{-21} & = &7 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & -18x-x& = &7+21 \\\Leftrightarrow & -19x& = &28 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{28}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-28}{19} & & \\ & V = \left\{ \frac{-28}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x-7)& = & 14 \color{red}{-} (-12-5x) \\\Leftrightarrow & -3x-21& = &14+12+5x \\\Leftrightarrow & -3x \color{red}{-21} & = &26 \color{red}{+5x} \\\Leftrightarrow & -3x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &26 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -3x-5x& = &26+21 \\\Leftrightarrow & -8x& = &47 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{47}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{-47}{8} & & \\ & V = \left\{ \frac{-47}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x+2)& = & -2 \color{red}{-} (-4+x) \\\Leftrightarrow & -12x+8& = &-2+4-x \\\Leftrightarrow & -12x \color{red}{+8} & = &2 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &2-8 \\\Leftrightarrow & -11x& = &-6 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-6}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-5x-7)& = & 7 \color{red}{+} (-15+x) \\\Leftrightarrow & -20x-28& = &7-15+x \\\Leftrightarrow & -20x \color{red}{-28} & = &-8 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -20x-x& = &-8+28 \\\Leftrightarrow & -21x& = &20 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{20}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-20}{21} & & \\ & V = \left\{ \frac{-20}{21} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x-3)& = & -15 \color{red}{-} (-8+2x) \\\Leftrightarrow & 3x-9& = &-15+8-2x \\\Leftrightarrow & 3x \color{red}{-9} & = &-7 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{-9} \color{blue}{+9} \color{blue}{+2x} & = &-7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+9} \\\Leftrightarrow & 3x+2x& = &-7+9 \\\Leftrightarrow & 5x& = &2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x-1)& = & -13 \color{red}{-} (-14+x) \\\Leftrightarrow & 30x-5& = &-13+14-x \\\Leftrightarrow & 30x \color{red}{-5} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-5} \color{blue}{+5} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+5} \\\Leftrightarrow & 30x+x& = &1+5 \\\Leftrightarrow & 31x& = &6 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{6}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (3x-2)& = & 11 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-8& = &11-1+x \\\Leftrightarrow & 12x \color{red}{-8} & = &10 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & 12x-x& = &10+8 \\\Leftrightarrow & 11x& = &18 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{18}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-5x+7)& = & -7 \color{red}{+} (11-3x) \\\Leftrightarrow & -10x+14& = &-7+11-3x \\\Leftrightarrow & -10x \color{red}{+14} & = &4 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-14} \\\Leftrightarrow & -10x+3x& = &4-14 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-2x+4)& = & 14 \color{red}{-} (5-3x) \\\Leftrightarrow & -4x+8& = &14-5+3x \\\Leftrightarrow & -4x \color{red}{+8} & = &9 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -4x-3x& = &9-8 \\\Leftrightarrow & -7x& = &1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x-2)& = & 15 \color{red}{-} (6-3x) \\\Leftrightarrow & 4x-4& = &15-6+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &9 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &9+4 \\\Leftrightarrow & x& = &13 \\ & V = \left\{ 13 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-2)& = & 2 \color{red}{-} (-4+x) \\\Leftrightarrow & -3x-6& = &2+4-x \\\Leftrightarrow & -3x \color{red}{-6} & = &6 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -3x+x& = &6+6 \\\Leftrightarrow & -2x& = &12 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{12}{ \color{red}{-2} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (3x-5)& = & -14 \color{red}{+} (-15+x) \\\Leftrightarrow & 18x-30& = &-14-15+x \\\Leftrightarrow & 18x \color{red}{-30} & = &-29 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-29 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 18x-x& = &-29+30 \\\Leftrightarrow & 17x& = &1 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{1}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{1}{17} & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)