Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x-2)& = & 6 \color{red}{-} (13-5x) \\\Leftrightarrow & -8x-4& = &6-13+5x \\\Leftrightarrow & -8x \color{red}{-4} & = &-7 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &-7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & -8x-5x& = &-7+4 \\\Leftrightarrow & -13x& = &-3 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-3}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (5x-7)& = & -14 \color{red}{-} (-15+x) \\\Leftrightarrow & 20x-28& = &-14+15-x \\\Leftrightarrow & 20x \color{red}{-28} & = &1 \color{red}{-x} \\\Leftrightarrow & 20x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 20x+x& = &1+28 \\\Leftrightarrow & 21x& = &29 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{29}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{29}{21} & & \\ & V = \left\{ \frac{29}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (4x+2)& = & 2 \color{red}{-} (9+x) \\\Leftrightarrow & 16x+8& = &2-9-x \\\Leftrightarrow & 16x \color{red}{+8} & = &-7 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 16x+x& = &-7-8 \\\Leftrightarrow & 17x& = &-15 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-15}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-15}{17} & & \\ & V = \left\{ \frac{-15}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-2x+6)& = & 5 \color{red}{+} (-10+x) \\\Leftrightarrow & -10x+30& = &5-10+x \\\Leftrightarrow & -10x \color{red}{+30} & = &-5 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & -10x-x& = &-5-30 \\\Leftrightarrow & -11x& = &-35 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-35}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{35}{11} & & \\ & V = \left\{ \frac{35}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+5)& = & 6 \color{red}{+} (-11-5x) \\\Leftrightarrow & 6x+30& = &6-11-5x \\\Leftrightarrow & 6x \color{red}{+30} & = &-5 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &-5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & 6x+5x& = &-5-30 \\\Leftrightarrow & 11x& = &-35 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-35}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-35}{11} & & \\ & V = \left\{ \frac{-35}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-3x-7)& = & 14 \color{red}{+} (10+4x) \\\Leftrightarrow & -9x-21& = &14+10+4x \\\Leftrightarrow & -9x \color{red}{-21} & = &24 \color{red}{+4x} \\\Leftrightarrow & -9x \color{red}{-21} \color{blue}{+21} \color{blue}{-4x} & = &24 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+21} \\\Leftrightarrow & -9x-4x& = &24+21 \\\Leftrightarrow & -13x& = &45 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{45}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-45}{13} & & \\ & V = \left\{ \frac{-45}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-2)& = & 15 \color{red}{-} (8+3x) \\\Leftrightarrow & 8x-8& = &15-8-3x \\\Leftrightarrow & 8x \color{red}{-8} & = &7 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & 8x+3x& = &7+8 \\\Leftrightarrow & 11x& = &15 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{15}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x+5)& = & 8 \color{red}{+} (-6+x) \\\Leftrightarrow & -20x+25& = &8-6+x \\\Leftrightarrow & -20x \color{red}{+25} & = &2 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -20x-x& = &2-25 \\\Leftrightarrow & -21x& = &-23 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-23}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{23}{21} & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x+1)& = & 4 \color{red}{-} (1+x) \\\Leftrightarrow & 30x+6& = &4-1-x \\\Leftrightarrow & 30x \color{red}{+6} & = &3 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 30x+x& = &3-6 \\\Leftrightarrow & 31x& = &-3 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-3}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-3}{31} & & \\ & V = \left\{ \frac{-3}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-6x-7)& = & -15 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x-14& = &-15-15+x \\\Leftrightarrow & -12x \color{red}{-14} & = &-30 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-14} \color{blue}{+14} \color{blue}{-x} & = &-30 \color{red}{+x} \color{blue}{-x} \color{blue}{+14} \\\Leftrightarrow & -12x-x& = &-30+14 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (6x-3)& = & -14 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x-6& = &-14+4-x \\\Leftrightarrow & 12x \color{red}{-6} & = &-10 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 12x+x& = &-10+6 \\\Leftrightarrow & 13x& = &-4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x-7)& = & -7 \color{red}{+} (5-5x) \\\Leftrightarrow & 18x-21& = &-7+5-5x \\\Leftrightarrow & 18x \color{red}{-21} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & 18x+5x& = &-2+21 \\\Leftrightarrow & 23x& = &19 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{19}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)