Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x-6)& = & -3 \color{red}{-} (1-2x) \\\Leftrightarrow & -5x-30& = &-3-1+2x \\\Leftrightarrow & -5x \color{red}{-30} & = &-4 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{-30} \color{blue}{+30} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+30} \\\Leftrightarrow & -5x-2x& = &-4+30 \\\Leftrightarrow & -7x& = &26 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{26}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-26}{7} & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (2x-3)& = & 14 \color{red}{-} (15+x) \\\Leftrightarrow & 10x-15& = &14-15-x \\\Leftrightarrow & 10x \color{red}{-15} & = &-1 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 10x+x& = &-1+15 \\\Leftrightarrow & 11x& = &14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x-7)& = & -5 \color{red}{+} (15+x) \\\Leftrightarrow & 4x-28& = &-5+15+x \\\Leftrightarrow & 4x \color{red}{-28} & = &10 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & 4x-x& = &10+28 \\\Leftrightarrow & 3x& = &38 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{38}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{38}{3} & & \\ & V = \left\{ \frac{38}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (6x+6)& = & -13 \color{red}{+} (-5+x) \\\Leftrightarrow & 36x+36& = &-13-5+x \\\Leftrightarrow & 36x \color{red}{+36} & = &-18 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 36x-x& = &-18-36 \\\Leftrightarrow & 35x& = &-54 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-54}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-54}{35} & & \\ & V = \left\{ \frac{-54}{35} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-4x+4)& = & 7 \color{red}{+} (-5-5x) \\\Leftrightarrow & -8x+8& = &7-5-5x \\\Leftrightarrow & -8x \color{red}{+8} & = &2 \color{red}{-5x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{+5x} & = &2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-8} \\\Leftrightarrow & -8x+5x& = &2-8 \\\Leftrightarrow & -3x& = &-6 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-6}{ \color{red}{-3} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (4x+2)& = & -5 \color{red}{-} (15-5x) \\\Leftrightarrow & 8x+4& = &-5-15+5x \\\Leftrightarrow & 8x \color{red}{+4} & = &-20 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+4} \color{blue}{-4} \color{blue}{-5x} & = &-20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-4} \\\Leftrightarrow & 8x-5x& = &-20-4 \\\Leftrightarrow & 3x& = &-24 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-24}{ \color{red}{3} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-2x-3)& = & 14 \color{red}{+} (8-3x) \\\Leftrightarrow & -4x-6& = &14+8-3x \\\Leftrightarrow & -4x \color{red}{-6} & = &22 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &22 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & -4x+3x& = &22+6 \\\Leftrightarrow & -x& = &28 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{28}{ \color{red}{-1} } \\\Leftrightarrow & x = -28 & & \\ & V = \left\{ -28 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x+2)& = & 14 \color{red}{+} (4-2x) \\\Leftrightarrow & 5x+10& = &14+4-2x \\\Leftrightarrow & 5x \color{red}{+10} & = &18 \color{red}{-2x} \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{+2x} & = &18 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-10} \\\Leftrightarrow & 5x+2x& = &18-10 \\\Leftrightarrow & 7x& = &8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (5x-4)& = & 5 \color{red}{+} (-11+3x) \\\Leftrightarrow & 25x-20& = &5-11+3x \\\Leftrightarrow & 25x \color{red}{-20} & = &-6 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 25x-3x& = &-6+20 \\\Leftrightarrow & 22x& = &14 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{14}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{7}{11} & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-4x-1)& = & -11 \color{red}{+} (-11+x) \\\Leftrightarrow & -12x-3& = &-11-11+x \\\Leftrightarrow & -12x \color{red}{-3} & = &-22 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &-22+3 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+1)& = & -11 \color{red}{-} (-14-3x) \\\Leftrightarrow & -4x+2& = &-11+14+3x \\\Leftrightarrow & -4x \color{red}{+2} & = &3 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+2} \color{blue}{-2} \color{blue}{-3x} & = &3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-2} \\\Leftrightarrow & -4x-3x& = &3-2 \\\Leftrightarrow & -7x& = &1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (5x+4)& = & -13 \color{red}{+} (-11+3x) \\\Leftrightarrow & 20x+16& = &-13-11+3x \\\Leftrightarrow & 20x \color{red}{+16} & = &-24 \color{red}{+3x} \\\Leftrightarrow & 20x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &-24 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 20x-3x& = &-24-16 \\\Leftrightarrow & 17x& = &-40 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-40}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-40}{17} & & \\ & V = \left\{ \frac{-40}{17} \right\} & \\\end{align}\)