Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x+7)& = & 15 \color{red}{+} (-1-2x) \\\Leftrightarrow & 9x+21& = &15-1-2x \\\Leftrightarrow & 9x \color{red}{+21} & = &14 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 9x+2x& = &14-21 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x+6)& = & -1 \color{red}{-} (9+x) \\\Leftrightarrow & -4x+12& = &-1-9-x \\\Leftrightarrow & -4x \color{red}{+12} & = &-10 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -4x+x& = &-10-12 \\\Leftrightarrow & -3x& = &-22 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-22}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{22}{3} & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (x+1)& = & 15 \color{red}{+} (5+x) \\\Leftrightarrow & 6x+6& = &15+5+x \\\Leftrightarrow & 6x \color{red}{+6} & = &20 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 6x-x& = &20-6 \\\Leftrightarrow & 5x& = &14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x+2)& = & -11 \color{red}{-} (-5+x) \\\Leftrightarrow & 2x+4& = &-11+5-x \\\Leftrightarrow & 2x \color{red}{+4} & = &-6 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & 2x+x& = &-6-4 \\\Leftrightarrow & 3x& = &-10 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-10}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x+6)& = & -1 \color{red}{-} (7+x) \\\Leftrightarrow & -12x+18& = &-1-7-x \\\Leftrightarrow & -12x \color{red}{+18} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &-8-18 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x+4)& = & -3 \color{red}{-} (-10+x) \\\Leftrightarrow & 12x+8& = &-3+10-x \\\Leftrightarrow & 12x \color{red}{+8} & = &7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 12x+x& = &7-8 \\\Leftrightarrow & 13x& = &-1 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-1}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x-6)& = & 11 \color{red}{+} (6+x) \\\Leftrightarrow & -10x-12& = &11+6+x \\\Leftrightarrow & -10x \color{red}{-12} & = &17 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &17 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -10x-x& = &17+12 \\\Leftrightarrow & -11x& = &29 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{29}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-29}{11} & & \\ & V = \left\{ \frac{-29}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x+5)& = & 9 \color{red}{-} (-10+x) \\\Leftrightarrow & -30x+25& = &9+10-x \\\Leftrightarrow & -30x \color{red}{+25} & = &19 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{+x} & = &19 \color{red}{-x} \color{blue}{+x} \color{blue}{-25} \\\Leftrightarrow & -30x+x& = &19-25 \\\Leftrightarrow & -29x& = &-6 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-6}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{6}{29} & & \\ & V = \left\{ \frac{6}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (-x-2)& = & 3 \color{red}{+} (-10+x) \\\Leftrightarrow & -3x-6& = &3-10+x \\\Leftrightarrow & -3x \color{red}{-6} & = &-7 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -3x-x& = &-7+6 \\\Leftrightarrow & -4x& = &-1 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{-1}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{1}{4} & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x-4)& = & -3 \color{red}{-} (5-2x) \\\Leftrightarrow & 15x-12& = &-3-5+2x \\\Leftrightarrow & 15x \color{red}{-12} & = &-8 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-8 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & 15x-2x& = &-8+12 \\\Leftrightarrow & 13x& = &4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{4}{13} & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x-2)& = & 10 \color{red}{+} (-14+x) \\\Leftrightarrow & -24x-8& = &10-14+x \\\Leftrightarrow & -24x \color{red}{-8} & = &-4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -24x-x& = &-4+8 \\\Leftrightarrow & -25x& = &4 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{4}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-4}{25} & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (5x+1)& = & 4 \color{red}{-} (-1+x) \\\Leftrightarrow & 30x+6& = &4+1-x \\\Leftrightarrow & 30x \color{red}{+6} & = &5 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &5 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 30x+x& = &5-6 \\\Leftrightarrow & 31x& = &-1 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-1}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-1}{31} & & \\ & V = \left\{ \frac{-1}{31} \right\} & \\\end{align}\)