Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-5x-6)& = & 5 \color{red}{-} (7-3x) \\\Leftrightarrow & -10x-12& = &5-7+3x \\\Leftrightarrow & -10x \color{red}{-12} & = &-2 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &-2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & -10x-3x& = &-2+12 \\\Leftrightarrow & -13x& = &10 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{10}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-10}{13} & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (5x+2)& = & -15 \color{red}{-} (-5+x) \\\Leftrightarrow & 30x+12& = &-15+5-x \\\Leftrightarrow & 30x \color{red}{+12} & = &-10 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 30x+x& = &-10-12 \\\Leftrightarrow & 31x& = &-22 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-22}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-22}{31} & & \\ & V = \left\{ \frac{-22}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x-2)& = & -6 \color{red}{-} (2+x) \\\Leftrightarrow & -24x-8& = &-6-2-x \\\Leftrightarrow & -24x \color{red}{-8} & = &-8 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & -24x+x& = &-8+8 \\\Leftrightarrow & -23x& = &0 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{0}{ \color{red}{-23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x-4)& = & 10 \color{red}{+} (-10+3x) \\\Leftrightarrow & 4x-8& = &10-10+3x \\\Leftrightarrow & 4x \color{red}{-8} & = &0 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 4x-3x& = &0+8 \\\Leftrightarrow & x& = &8 \\ & V = \left\{ 8 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x+7)& = & -12 \color{red}{+} (-3+x) \\\Leftrightarrow & 3x+21& = &-12-3+x \\\Leftrightarrow & 3x \color{red}{+21} & = &-15 \color{red}{+x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 3x-x& = &-15-21 \\\Leftrightarrow & 2x& = &-36 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-36}{ \color{red}{2} } \\\Leftrightarrow & x = -18 & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+1)& = & 8 \color{red}{-} (1+x) \\\Leftrightarrow & -15x+5& = &8-1-x \\\Leftrightarrow & -15x \color{red}{+5} & = &7 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+5} \color{blue}{-5} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-5} \\\Leftrightarrow & -15x+x& = &7-5 \\\Leftrightarrow & -14x& = &2 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{2}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-5x+7)& = & 1 \color{red}{+} (13-2x) \\\Leftrightarrow & -15x+21& = &1+13-2x \\\Leftrightarrow & -15x \color{red}{+21} & = &14 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &14 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & -15x+2x& = &14-21 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (4x+5)& = & -2 \color{red}{+} (15+x) \\\Leftrightarrow & 24x+30& = &-2+15+x \\\Leftrightarrow & 24x \color{red}{+30} & = &13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 24x-x& = &13-30 \\\Leftrightarrow & 23x& = &-17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-17}{23} & & \\ & V = \left\{ \frac{-17}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x+4)& = & -10 \color{red}{+} (4+x) \\\Leftrightarrow & 9x+12& = &-10+4+x \\\Leftrightarrow & 9x \color{red}{+12} & = &-6 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-6 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 9x-x& = &-6-12 \\\Leftrightarrow & 8x& = &-18 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{-18}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{-9}{4} & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (5x-3)& = & 2 \color{red}{-} (10+x) \\\Leftrightarrow & 30x-18& = &2-10-x \\\Leftrightarrow & 30x \color{red}{-18} & = &-8 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &-8+18 \\\Leftrightarrow & 31x& = &10 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{10}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x+4)& = & -3 \color{red}{-} (-11+x) \\\Leftrightarrow & 18x+24& = &-3+11-x \\\Leftrightarrow & 18x \color{red}{+24} & = &8 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 18x+x& = &8-24 \\\Leftrightarrow & 19x& = &-16 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-16}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-16}{19} & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-x+1)& = & -8 \color{red}{+} (14-5x) \\\Leftrightarrow & -6x+6& = &-8+14-5x \\\Leftrightarrow & -6x \color{red}{+6} & = &6 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & -6x+5x& = &6-6 \\\Leftrightarrow & -x& = &0 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{0}{ \color{red}{-1} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)