Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-2x+7)& = & 2 \color{red}{+} (-14+x) \\\Leftrightarrow & -10x+35& = &2-14+x \\\Leftrightarrow & -10x \color{red}{+35} & = &-12 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & -10x-x& = &-12-35 \\\Leftrightarrow & -11x& = &-47 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-47}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{47}{11} & & \\ & V = \left\{ \frac{47}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x-5)& = & 3 \color{red}{-} (-11-3x) \\\Leftrightarrow & -4x-10& = &3+11+3x \\\Leftrightarrow & -4x \color{red}{-10} & = &14 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -4x-3x& = &14+10 \\\Leftrightarrow & -7x& = &24 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{24}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-24}{7} & & \\ & V = \left\{ \frac{-24}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x+4)& = & -14 \color{red}{+} (14+x) \\\Leftrightarrow & -4x+16& = &-14+14+x \\\Leftrightarrow & -4x \color{red}{+16} & = &0 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -4x-x& = &0-16 \\\Leftrightarrow & -5x& = &-16 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-16}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (2x-4)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & 10x-20& = &11-10-x \\\Leftrightarrow & 10x \color{red}{-20} & = &1 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 10x+x& = &1+20 \\\Leftrightarrow & 11x& = &21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-3x+4)& = & 10 \color{red}{-} (-5+x) \\\Leftrightarrow & -6x+8& = &10+5-x \\\Leftrightarrow & -6x \color{red}{+8} & = &15 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -6x+x& = &15-8 \\\Leftrightarrow & -5x& = &7 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{7}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x-4)& = & 9 \color{red}{-} (-3+x) \\\Leftrightarrow & 30x-20& = &9+3-x \\\Leftrightarrow & 30x \color{red}{-20} & = &12 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 30x+x& = &12+20 \\\Leftrightarrow & 31x& = &32 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{32}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{32}{31} & & \\ & V = \left\{ \frac{32}{31} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-2)& = & -6 \color{red}{+} (6-5x) \\\Leftrightarrow & 8x-8& = &-6+6-5x \\\Leftrightarrow & 8x \color{red}{-8} & = &0 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+8} \\\Leftrightarrow & 8x+5x& = &0+8 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-5x+4)& = & 5 \color{red}{+} (-12+x) \\\Leftrightarrow & -25x+20& = &5-12+x \\\Leftrightarrow & -25x \color{red}{+20} & = &-7 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & -25x-x& = &-7-20 \\\Leftrightarrow & -26x& = &-27 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{-27}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{27}{26} & & \\ & V = \left\{ \frac{27}{26} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x+4)& = & -2 \color{red}{-} (-11-5x) \\\Leftrightarrow & 18x+12& = &-2+11+5x \\\Leftrightarrow & 18x \color{red}{+12} & = &9 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 18x-5x& = &9-12 \\\Leftrightarrow & 13x& = &-3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (2x+7)& = & 13 \color{red}{+} (8+x) \\\Leftrightarrow & 6x+21& = &13+8+x \\\Leftrightarrow & 6x \color{red}{+21} & = &21 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &21 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 6x-x& = &21-21 \\\Leftrightarrow & 5x& = &0 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{0}{ \color{red}{5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+2)& = & 3 \color{red}{+} (15+x) \\\Leftrightarrow & -4x+4& = &3+15+x \\\Leftrightarrow & -4x \color{red}{+4} & = &18 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -4x-x& = &18-4 \\\Leftrightarrow & -5x& = &14 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{14}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x+7)& = & -3 \color{red}{-} (7+x) \\\Leftrightarrow & -2x+14& = &-3-7-x \\\Leftrightarrow & -2x \color{red}{+14} & = &-10 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -2x+x& = &-10-14 \\\Leftrightarrow & -x& = &-24 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-24}{ \color{red}{-1} } \\\Leftrightarrow & x = 24 & & \\ & V = \left\{ 24 \right\} & \\\end{align}\)