Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (3x-1)& = & -14 \color{red}{+} (5-5x) \\\Leftrightarrow & 6x-2& = &-14+5-5x \\\Leftrightarrow & 6x \color{red}{-2} & = &-9 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-2} \color{blue}{+2} \color{blue}{+5x} & = &-9 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+2} \\\Leftrightarrow & 6x+5x& = &-9+2 \\\Leftrightarrow & 11x& = &-7 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-7}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-x-6)& = & 10 \color{red}{+} (-3+x) \\\Leftrightarrow & -3x-18& = &10-3+x \\\Leftrightarrow & -3x \color{red}{-18} & = &7 \color{red}{+x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -3x-x& = &7+18 \\\Leftrightarrow & -4x& = &25 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = &\frac{25}{ \color{red}{-4} } \\\Leftrightarrow & x = \frac{-25}{4} & & \\ & V = \left\{ \frac{-25}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x-4)& = & 6 \color{red}{+} (-10+x) \\\Leftrightarrow & -30x-24& = &6-10+x \\\Leftrightarrow & -30x \color{red}{-24} & = &-4 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -30x-x& = &-4+24 \\\Leftrightarrow & -31x& = &20 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{20}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-20}{31} & & \\ & V = \left\{ \frac{-20}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x+3)& = & 7 \color{red}{-} (-10-2x) \\\Leftrightarrow & 25x+15& = &7+10+2x \\\Leftrightarrow & 25x \color{red}{+15} & = &17 \color{red}{+2x} \\\Leftrightarrow & 25x \color{red}{+15} \color{blue}{-15} \color{blue}{-2x} & = &17 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-15} \\\Leftrightarrow & 25x-2x& = &17-15 \\\Leftrightarrow & 23x& = &2 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{2}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-3)& = & -10 \color{red}{-} (-8-3x) \\\Leftrightarrow & 4x-12& = &-10+8+3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-2 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & 4x-3x& = &-2+12 \\\Leftrightarrow & x& = &10 \\ & V = \left\{ 10 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x-2)& = & -13 \color{red}{-} (11+x) \\\Leftrightarrow & -24x-8& = &-13-11-x \\\Leftrightarrow & -24x \color{red}{-8} & = &-24 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-24 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &-24+8 \\\Leftrightarrow & -23x& = &-16 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-16}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x-2)& = & -5 \color{red}{+} (15+x) \\\Leftrightarrow & -10x-4& = &-5+15+x \\\Leftrightarrow & -10x \color{red}{-4} & = &10 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &10 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & -10x-x& = &10+4 \\\Leftrightarrow & -11x& = &14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (3x+6)& = & 9 \color{red}{+} (-8-5x) \\\Leftrightarrow & 6x+12& = &9-8-5x \\\Leftrightarrow & 6x \color{red}{+12} & = &1 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 6x+5x& = &1-12 \\\Leftrightarrow & 11x& = &-11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-11}{ \color{red}{11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-3x+5)& = & -7 \color{red}{-} (1+x) \\\Leftrightarrow & -12x+20& = &-7-1-x \\\Leftrightarrow & -12x \color{red}{+20} & = &-8 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -12x+x& = &-8-20 \\\Leftrightarrow & -11x& = &-28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{28}{11} & & \\ & V = \left\{ \frac{28}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (3x-1)& = & 5 \color{red}{-} (-8+x) \\\Leftrightarrow & 12x-4& = &5+8-x \\\Leftrightarrow & 12x \color{red}{-4} & = &13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 12x+x& = &13+4 \\\Leftrightarrow & 13x& = &17 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{17}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+2)& = & 11 \color{red}{-} (-11+x) \\\Leftrightarrow & 36x+12& = &11+11-x \\\Leftrightarrow & 36x \color{red}{+12} & = &22 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 36x+x& = &22-12 \\\Leftrightarrow & 37x& = &10 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{10}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{10}{37} & & \\ & V = \left\{ \frac{10}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+4)& = & 5 \color{red}{+} (7-3x) \\\Leftrightarrow & 10x+20& = &5+7-3x \\\Leftrightarrow & 10x \color{red}{+20} & = &12 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 10x+3x& = &12-20 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)