Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-x-7)& = & -10 \color{red}{-} (-13-2x) \\\Leftrightarrow & -5x-35& = &-10+13+2x \\\Leftrightarrow & -5x \color{red}{-35} & = &3 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &3 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & -5x-2x& = &3+35 \\\Leftrightarrow & -7x& = &38 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{38}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-38}{7} & & \\ & V = \left\{ \frac{-38}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-1)& = & 11 \color{red}{-} (2+4x) \\\Leftrightarrow & 5x-5& = &11-2-4x \\\Leftrightarrow & 5x \color{red}{-5} & = &9 \color{red}{-4x} \\\Leftrightarrow & 5x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &9 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & 5x+4x& = &9+5 \\\Leftrightarrow & 9x& = &14 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{14}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{14}{9} & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (5x+6)& = & 11 \color{red}{-} (7-3x) \\\Leftrightarrow & 10x+12& = &11-7+3x \\\Leftrightarrow & 10x \color{red}{+12} & = &4 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &4 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & 10x-3x& = &4-12 \\\Leftrightarrow & 7x& = &-8 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-8}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-4x-3)& = & 13 \color{red}{+} (-6+x) \\\Leftrightarrow & -12x-9& = &13-6+x \\\Leftrightarrow & -12x \color{red}{-9} & = &7 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+9} \\\Leftrightarrow & -12x-x& = &7+9 \\\Leftrightarrow & -13x& = &16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (6x-5)& = & 13 \color{red}{+} (-4+x) \\\Leftrightarrow & 12x-10& = &13-4+x \\\Leftrightarrow & 12x \color{red}{-10} & = &9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 12x-x& = &9+10 \\\Leftrightarrow & 11x& = &19 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{19}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{19}{11} & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-7)& = & -7 \color{red}{-} (5+x) \\\Leftrightarrow & -6x-42& = &-7-5-x \\\Leftrightarrow & -6x \color{red}{-42} & = &-12 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -6x+x& = &-12+42 \\\Leftrightarrow & -5x& = &30 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{30}{ \color{red}{-5} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+4)& = & 5 \color{red}{-} (-15+4x) \\\Leftrightarrow & -5x+20& = &5+15-4x \\\Leftrightarrow & -5x \color{red}{+20} & = &20 \color{red}{-4x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{+4x} & = &20 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-20} \\\Leftrightarrow & -5x+4x& = &20-20 \\\Leftrightarrow & -x& = &0 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{0}{ \color{red}{-1} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+5)& = & 14 \color{red}{-} (11+x) \\\Leftrightarrow & 6x+30& = &14-11-x \\\Leftrightarrow & 6x \color{red}{+30} & = &3 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 6x+x& = &3-30 \\\Leftrightarrow & 7x& = &-27 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-27}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-27}{7} & & \\ & V = \left\{ \frac{-27}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-5)& = & -10 \color{red}{+} (10+x) \\\Leftrightarrow & 12x-30& = &-10+10+x \\\Leftrightarrow & 12x \color{red}{-30} & = &0 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 12x-x& = &0+30 \\\Leftrightarrow & 11x& = &30 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{30}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (x+7)& = & -5 \color{red}{-} (-5+x) \\\Leftrightarrow & 4x+28& = &-5+5-x \\\Leftrightarrow & 4x \color{red}{+28} & = &0 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 4x+x& = &0-28 \\\Leftrightarrow & 5x& = &-28 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-28}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-28}{5} & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x-5)& = & 15 \color{red}{-} (-7+4x) \\\Leftrightarrow & -3x-15& = &15+7-4x \\\Leftrightarrow & -3x \color{red}{-15} & = &22 \color{red}{-4x} \\\Leftrightarrow & -3x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &22 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -3x+4x& = &22+15 \\\Leftrightarrow & x& = &37 \\ & V = \left\{ 37 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x+4)& = & -14 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x+16& = &-14+7-x \\\Leftrightarrow & 12x \color{red}{+16} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 12x+x& = &-7-16 \\\Leftrightarrow & 13x& = &-23 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-23}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)