Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-6x+2)& = & 8 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x+4& = &8-15+x \\\Leftrightarrow & -12x \color{red}{+4} & = &-7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -12x-x& = &-7-4 \\\Leftrightarrow & -13x& = &-11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{11}{13} & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-6x-4)& = & -10 \color{red}{-} (-11+x) \\\Leftrightarrow & -24x-16& = &-10+11-x \\\Leftrightarrow & -24x \color{red}{-16} & = &1 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -24x+x& = &1+16 \\\Leftrightarrow & -23x& = &17 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{17}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-17}{23} & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x-7)& = & 13 \color{red}{-} (14+x) \\\Leftrightarrow & 8x-28& = &13-14-x \\\Leftrightarrow & 8x \color{red}{-28} & = &-1 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 8x+x& = &-1+28 \\\Leftrightarrow & 9x& = &27 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{27}{ \color{red}{9} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-2x+6)& = & 14 \color{red}{+} (14+x) \\\Leftrightarrow & -8x+24& = &14+14+x \\\Leftrightarrow & -8x \color{red}{+24} & = &28 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &28 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -8x-x& = &28-24 \\\Leftrightarrow & -9x& = &4 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{4}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x+1)& = & -6 \color{red}{-} (-7+x) \\\Leftrightarrow & 18x+6& = &-6+7-x \\\Leftrightarrow & 18x \color{red}{+6} & = &1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 18x+x& = &1-6 \\\Leftrightarrow & 19x& = &-5 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-5}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-5}{19} & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (-2x-3)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & -6x-9& = &6-11+x \\\Leftrightarrow & -6x \color{red}{-9} & = &-5 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -6x-x& = &-5+9 \\\Leftrightarrow & -7x& = &4 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{4}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x+7)& = & -5 \color{red}{-} (-14+4x) \\\Leftrightarrow & -15x+35& = &-5+14-4x \\\Leftrightarrow & -15x \color{red}{+35} & = &9 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & -15x+4x& = &9-35 \\\Leftrightarrow & -11x& = &-26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (5x+2)& = & 8 \color{red}{+} (-11+x) \\\Leftrightarrow & 15x+6& = &8-11+x \\\Leftrightarrow & 15x \color{red}{+6} & = &-3 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &-3 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & 15x-x& = &-3-6 \\\Leftrightarrow & 14x& = &-9 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-9}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-9}{14} & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (3x-2)& = & -8 \color{red}{-} (-14+x) \\\Leftrightarrow & 12x-8& = &-8+14-x \\\Leftrightarrow & 12x \color{red}{-8} & = &6 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 12x+x& = &6+8 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (2x-2)& = & 3 \color{red}{+} (-6+3x) \\\Leftrightarrow & 8x-8& = &3-6+3x \\\Leftrightarrow & 8x \color{red}{-8} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 8x-3x& = &-3+8 \\\Leftrightarrow & 5x& = &5 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{5}{ \color{red}{5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (2x+4)& = & -11 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x+24& = &-11+7-x \\\Leftrightarrow & 12x \color{red}{+24} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 12x+x& = &-4-24 \\\Leftrightarrow & 13x& = &-28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x+7)& = & -7 \color{red}{+} (-3+x) \\\Leftrightarrow & -12x+21& = &-7-3+x \\\Leftrightarrow & -12x \color{red}{+21} & = &-10 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & -12x-x& = &-10-21 \\\Leftrightarrow & -13x& = &-31 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-31}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{31}{13} & & \\ & V = \left\{ \frac{31}{13} \right\} & \\\end{align}\)