Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x+1)& = & -9 \color{red}{+} (10-5x) \\\Leftrightarrow & -6x+2& = &-9+10-5x \\\Leftrightarrow & -6x \color{red}{+2} & = &1 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+2} \color{blue}{-2} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-2} \\\Leftrightarrow & -6x+5x& = &1-2 \\\Leftrightarrow & -x& = &-1 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-1}{ \color{red}{-1} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-6)& = & -13 \color{red}{-} (-2-5x) \\\Leftrightarrow & 3x-18& = &-13+2+5x \\\Leftrightarrow & 3x \color{red}{-18} & = &-11 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 3x-5x& = &-11+18 \\\Leftrightarrow & -2x& = &7 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{7}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-7}{2} & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-4x+7)& = & 11 \color{red}{+} (13+x) \\\Leftrightarrow & -24x+42& = &11+13+x \\\Leftrightarrow & -24x \color{red}{+42} & = &24 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &24 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & -24x-x& = &24-42 \\\Leftrightarrow & -25x& = &-18 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-18}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{18}{25} & & \\ & V = \left\{ \frac{18}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (-6x-4)& = & 6 \color{red}{-} (14+x) \\\Leftrightarrow & -12x-8& = &6-14-x \\\Leftrightarrow & -12x \color{red}{-8} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -12x+x& = &-8+8 \\\Leftrightarrow & -11x& = &0 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{0}{ \color{red}{-11} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (6x+5)& = & -12 \color{red}{+} (-4+x) \\\Leftrightarrow & 36x+30& = &-12-4+x \\\Leftrightarrow & 36x \color{red}{+30} & = &-16 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 36x-x& = &-16-30 \\\Leftrightarrow & 35x& = &-46 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-46}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-46}{35} & & \\ & V = \left\{ \frac{-46}{35} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-1)& = & -15 \color{red}{+} (8+x) \\\Leftrightarrow & 18x-6& = &-15+8+x \\\Leftrightarrow & 18x \color{red}{-6} & = &-7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 18x-x& = &-7+6 \\\Leftrightarrow & 17x& = &-1 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-1}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (2x-5)& = & 12 \color{red}{-} (5+x) \\\Leftrightarrow & 10x-25& = &12-5-x \\\Leftrightarrow & 10x \color{red}{-25} & = &7 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 10x+x& = &7+25 \\\Leftrightarrow & 11x& = &32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (5x+1)& = & 12 \color{red}{-} (14+3x) \\\Leftrightarrow & 20x+4& = &12-14-3x \\\Leftrightarrow & 20x \color{red}{+4} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 20x+3x& = &-2-4 \\\Leftrightarrow & 23x& = &-6 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-6}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (2x+6)& = & 3 \color{red}{-} (-15+x) \\\Leftrightarrow & 10x+30& = &3+15-x \\\Leftrightarrow & 10x \color{red}{+30} & = &18 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &18 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 10x+x& = &18-30 \\\Leftrightarrow & 11x& = &-12 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-12}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-12}{11} & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (6x+7)& = & -11 \color{red}{+} (-8+x) \\\Leftrightarrow & 24x+28& = &-11-8+x \\\Leftrightarrow & 24x \color{red}{+28} & = &-19 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &-19 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 24x-x& = &-19-28 \\\Leftrightarrow & 23x& = &-47 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-47}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-47}{23} & & \\ & V = \left\{ \frac{-47}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-6x+3)& = & -10 \color{red}{+} (9+x) \\\Leftrightarrow & -24x+12& = &-10+9+x \\\Leftrightarrow & -24x \color{red}{+12} & = &-1 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -24x-x& = &-1-12 \\\Leftrightarrow & -25x& = &-13 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-13}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{13}{25} & & \\ & V = \left\{ \frac{13}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+4)& = & 12 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x+12& = &12-6+x \\\Leftrightarrow & -12x \color{red}{+12} & = &6 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &6-12 \\\Leftrightarrow & -13x& = &-6 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-6}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{6}{13} & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)