Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-4x+7)& = & 11 \color{red}{-} (5+x) \\\Leftrightarrow & -12x+21& = &11-5-x \\\Leftrightarrow & -12x \color{red}{+21} & = &6 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & -12x+x& = &6-21 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (x-3)& = & 9 \color{red}{-} (-15-4x) \\\Leftrightarrow & 5x-15& = &9+15+4x \\\Leftrightarrow & 5x \color{red}{-15} & = &24 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{-15} \color{blue}{+15} \color{blue}{-4x} & = &24 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+15} \\\Leftrightarrow & 5x-4x& = &24+15 \\\Leftrightarrow & x& = &39 \\ & V = \left\{ 39 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (x+2)& = & -6 \color{red}{-} (13-3x) \\\Leftrightarrow & 4x+8& = &-6-13+3x \\\Leftrightarrow & 4x \color{red}{+8} & = &-19 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 4x-3x& = &-19-8 \\\Leftrightarrow & x& = &-27 \\ & V = \left\{ -27 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-6x+7)& = & -9 \color{red}{-} (5-5x) \\\Leftrightarrow & -18x+21& = &-9-5+5x \\\Leftrightarrow & -18x \color{red}{+21} & = &-14 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & -18x-5x& = &-14-21 \\\Leftrightarrow & -23x& = &-35 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-35}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{35}{23} & & \\ & V = \left\{ \frac{35}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-3x+1)& = & -8 \color{red}{-} (13-5x) \\\Leftrightarrow & -18x+6& = &-8-13+5x \\\Leftrightarrow & -18x \color{red}{+6} & = &-21 \color{red}{+5x} \\\Leftrightarrow & -18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &-21 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & -18x-5x& = &-21-6 \\\Leftrightarrow & -23x& = &-27 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-27}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{27}{23} & & \\ & V = \left\{ \frac{27}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x+1)& = & -2 \color{red}{-} (15+x) \\\Leftrightarrow & -12x+6& = &-2-15-x \\\Leftrightarrow & -12x \color{red}{+6} & = &-17 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-17 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &-17-6 \\\Leftrightarrow & -11x& = &-23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{23}{11} & & \\ & V = \left\{ \frac{23}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (x+7)& = & -1 \color{red}{-} (-15+x) \\\Leftrightarrow & 4x+28& = &-1+15-x \\\Leftrightarrow & 4x \color{red}{+28} & = &14 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 4x+x& = &14-28 \\\Leftrightarrow & 5x& = &-14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-5)& = & 1 \color{red}{-} (1+x) \\\Leftrightarrow & -6x-30& = &1-1-x \\\Leftrightarrow & -6x \color{red}{-30} & = &0 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -6x+x& = &0+30 \\\Leftrightarrow & -5x& = &30 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{30}{ \color{red}{-5} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-2x-6)& = & -6 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-36& = &-6-7-x \\\Leftrightarrow & -12x \color{red}{-36} & = &-13 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & -12x+x& = &-13+36 \\\Leftrightarrow & -11x& = &23 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{23}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (6x+5)& = & -5 \color{red}{+} (13+x) \\\Leftrightarrow & 12x+10& = &-5+13+x \\\Leftrightarrow & 12x \color{red}{+10} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 12x-x& = &8-10 \\\Leftrightarrow & 11x& = &-2 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-2}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-x-7)& = & -2 \color{red}{+} (-15+x) \\\Leftrightarrow & -6x-42& = &-2-15+x \\\Leftrightarrow & -6x \color{red}{-42} & = &-17 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -6x-x& = &-17+42 \\\Leftrightarrow & -7x& = &25 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{25}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-25}{7} & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-4x-1)& = & -10 \color{red}{+} (-15+x) \\\Leftrightarrow & -12x-3& = &-10-15+x \\\Leftrightarrow & -12x \color{red}{-3} & = &-25 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{+3} \\\Leftrightarrow & -12x-x& = &-25+3 \\\Leftrightarrow & -13x& = &-22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{22}{13} & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)