Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (4x-7)& = & 6 \color{red}{+} (5+x) \\\Leftrightarrow & 12x-21& = &6+5+x \\\Leftrightarrow & 12x \color{red}{-21} & = &11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 12x-x& = &11+21 \\\Leftrightarrow & 11x& = &32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x+1)& = & -6 \color{red}{-} (-14+x) \\\Leftrightarrow & 6x+6& = &-6+14-x \\\Leftrightarrow & 6x \color{red}{+6} & = &8 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 6x+x& = &8-6 \\\Leftrightarrow & 7x& = &2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (2x+3)& = & 4 \color{red}{+} (15+x) \\\Leftrightarrow & 8x+12& = &4+15+x \\\Leftrightarrow & 8x \color{red}{+12} & = &19 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 8x-x& = &19-12 \\\Leftrightarrow & 7x& = &7 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{7}{ \color{red}{7} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-3x-6)& = & -9 \color{red}{-} (-7+4x) \\\Leftrightarrow & -9x-18& = &-9+7-4x \\\Leftrightarrow & -9x \color{red}{-18} & = &-2 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-18} \color{blue}{+18} \color{blue}{+4x} & = &-2 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+18} \\\Leftrightarrow & -9x+4x& = &-2+18 \\\Leftrightarrow & -5x& = &16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-16}{5} & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x-2)& = & -15 \color{red}{-} (-4+x) \\\Leftrightarrow & 30x-12& = &-15+4-x \\\Leftrightarrow & 30x \color{red}{-12} & = &-11 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 30x+x& = &-11+12 \\\Leftrightarrow & 31x& = &1 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{1}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{1}{31} & & \\ & V = \left\{ \frac{1}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-1)& = & -7 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x-4& = &-7-4+x \\\Leftrightarrow & -24x \color{red}{-4} & = &-11 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -24x-x& = &-11+4 \\\Leftrightarrow & -25x& = &-7 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-7}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{7}{25} & & \\ & V = \left\{ \frac{7}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (2x-5)& = & -2 \color{red}{+} (13-5x) \\\Leftrightarrow & 6x-15& = &-2+13-5x \\\Leftrightarrow & 6x \color{red}{-15} & = &11 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &11 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 6x+5x& = &11+15 \\\Leftrightarrow & 11x& = &26 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{26}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{26}{11} & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-3x+3)& = & 14 \color{red}{+} (-3-2x) \\\Leftrightarrow & -9x+9& = &14-3-2x \\\Leftrightarrow & -9x \color{red}{+9} & = &11 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{+9} \color{blue}{-9} \color{blue}{+2x} & = &11 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-9} \\\Leftrightarrow & -9x+2x& = &11-9 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (6x+7)& = & -3 \color{red}{+} (10+x) \\\Leftrightarrow & 24x+28& = &-3+10+x \\\Leftrightarrow & 24x \color{red}{+28} & = &7 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & 24x-x& = &7-28 \\\Leftrightarrow & 23x& = &-21 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-21}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-21}{23} & & \\ & V = \left\{ \frac{-21}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x-2)& = & 9 \color{red}{-} (-7+3x) \\\Leftrightarrow & 10x-10& = &9+7-3x \\\Leftrightarrow & 10x \color{red}{-10} & = &16 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{+3x} & = &16 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+10} \\\Leftrightarrow & 10x+3x& = &16+10 \\\Leftrightarrow & 13x& = &26 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{26}{ \color{red}{13} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x+6)& = & -12 \color{red}{+} (7-4x) \\\Leftrightarrow & 9x+18& = &-12+7-4x \\\Leftrightarrow & 9x \color{red}{+18} & = &-5 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+18} \color{blue}{-18} \color{blue}{+4x} & = &-5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-18} \\\Leftrightarrow & 9x+4x& = &-5-18 \\\Leftrightarrow & 13x& = &-23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-3x+7)& = & -3 \color{red}{-} (11+4x) \\\Leftrightarrow & -15x+35& = &-3-11-4x \\\Leftrightarrow & -15x \color{red}{+35} & = &-14 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{+35} \color{blue}{-35} \color{blue}{+4x} & = &-14 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-35} \\\Leftrightarrow & -15x+4x& = &-14-35 \\\Leftrightarrow & -11x& = &-49 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-49}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{49}{11} & & \\ & V = \left\{ \frac{49}{11} \right\} & \\\end{align}\)