Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (x-4)& = & -14 \color{red}{+} (-6+4x) \\\Leftrightarrow & 5x-20& = &-14-6+4x \\\Leftrightarrow & 5x \color{red}{-20} & = &-20 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-20} \color{blue}{+20} \color{blue}{-4x} & = &-20 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+20} \\\Leftrightarrow & 5x-4x& = &-20+20 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x+5)& = & 15 \color{red}{+} (-9-5x) \\\Leftrightarrow & 18x+30& = &15-9-5x \\\Leftrightarrow & 18x \color{red}{+30} & = &6 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & 18x+5x& = &6-30 \\\Leftrightarrow & 23x& = &-24 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-24}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-24}{23} & & \\ & V = \left\{ \frac{-24}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x-7)& = & -4 \color{red}{+} (2+2x) \\\Leftrightarrow & 5x-35& = &-4+2+2x \\\Leftrightarrow & 5x \color{red}{-35} & = &-2 \color{red}{+2x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &-2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & 5x-2x& = &-2+35 \\\Leftrightarrow & 3x& = &33 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{33}{ \color{red}{3} } \\\Leftrightarrow & x = 11 & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (2x+1)& = & 6 \color{red}{-} (4+x) \\\Leftrightarrow & 12x+6& = &6-4-x \\\Leftrightarrow & 12x \color{red}{+6} & = &2 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &2 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &2-6 \\\Leftrightarrow & 13x& = &-4 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-4}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x-6)& = & -9 \color{red}{+} (-5-3x) \\\Leftrightarrow & 4x-12& = &-9-5-3x \\\Leftrightarrow & 4x \color{red}{-12} & = &-14 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 4x+3x& = &-14+12 \\\Leftrightarrow & 7x& = &-2 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-2}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x+7)& = & -11 \color{red}{+} (-13+x) \\\Leftrightarrow & 12x+14& = &-11-13+x \\\Leftrightarrow & 12x \color{red}{+14} & = &-24 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-24 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & 12x-x& = &-24-14 \\\Leftrightarrow & 11x& = &-38 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-38}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-38}{11} & & \\ & V = \left\{ \frac{-38}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (6x+6)& = & -11 \color{red}{+} (7+x) \\\Leftrightarrow & 12x+12& = &-11+7+x \\\Leftrightarrow & 12x \color{red}{+12} & = &-4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 12x-x& = &-4-12 \\\Leftrightarrow & 11x& = &-16 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-16}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-16}{11} & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-6x+4)& = & -4 \color{red}{+} (10+x) \\\Leftrightarrow & -30x+20& = &-4+10+x \\\Leftrightarrow & -30x \color{red}{+20} & = &6 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -30x-x& = &6-20 \\\Leftrightarrow & -31x& = &-14 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-14}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{14}{31} & & \\ & V = \left\{ \frac{14}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+7)& = & 2 \color{red}{+} (3-4x) \\\Leftrightarrow & 9x+21& = &2+3-4x \\\Leftrightarrow & 9x \color{red}{+21} & = &5 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{+21} \color{blue}{-21} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-21} \\\Leftrightarrow & 9x+4x& = &5-21 \\\Leftrightarrow & 13x& = &-16 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-16}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x+3)& = & -12 \color{red}{-} (-7-5x) \\\Leftrightarrow & 3x+9& = &-12+7+5x \\\Leftrightarrow & 3x \color{red}{+9} & = &-5 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &-5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 3x-5x& = &-5-9 \\\Leftrightarrow & -2x& = &-14 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{-14}{ \color{red}{-2} } \\\Leftrightarrow & x = 7 & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-4)& = & 10 \color{red}{-} (11-2x) \\\Leftrightarrow & -3x-12& = &10-11+2x \\\Leftrightarrow & -3x \color{red}{-12} & = &-1 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-12} \color{blue}{+12} \color{blue}{-2x} & = &-1 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+12} \\\Leftrightarrow & -3x-2x& = &-1+12 \\\Leftrightarrow & -5x& = &11 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{11}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-11}{5} & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (2x+6)& = & 5 \color{red}{-} (-1-3x) \\\Leftrightarrow & 10x+30& = &5+1+3x \\\Leftrightarrow & 10x \color{red}{+30} & = &6 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & 10x-3x& = &6-30 \\\Leftrightarrow & 7x& = &-24 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-24}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)