Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x-2)& = & -5 \color{red}{+} (4-5x) \\\Leftrightarrow & 8x-4& = &-5+4-5x \\\Leftrightarrow & 8x \color{red}{-4} & = &-1 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{-4} \color{blue}{+4} \color{blue}{+5x} & = &-1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+4} \\\Leftrightarrow & 8x+5x& = &-1+4 \\\Leftrightarrow & 13x& = &3 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{3}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x-6)& = & -3 \color{red}{-} (-7+x) \\\Leftrightarrow & 9x-18& = &-3+7-x \\\Leftrightarrow & 9x \color{red}{-18} & = &4 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 9x+x& = &4+18 \\\Leftrightarrow & 10x& = &22 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{22}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{11}{5} & & \\ & V = \left\{ \frac{11}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x-6)& = & -14 \color{red}{+} (-1+x) \\\Leftrightarrow & -30x-36& = &-14-1+x \\\Leftrightarrow & -30x \color{red}{-36} & = &-15 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & -30x-x& = &-15+36 \\\Leftrightarrow & -31x& = &21 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{21}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-21}{31} & & \\ & V = \left\{ \frac{-21}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (5x-1)& = & 1 \color{red}{-} (11+4x) \\\Leftrightarrow & 25x-5& = &1-11-4x \\\Leftrightarrow & 25x \color{red}{-5} & = &-10 \color{red}{-4x} \\\Leftrightarrow & 25x \color{red}{-5} \color{blue}{+5} \color{blue}{+4x} & = &-10 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+5} \\\Leftrightarrow & 25x+4x& = &-10+5 \\\Leftrightarrow & 29x& = &-5 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-5}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-5}{29} & & \\ & V = \left\{ \frac{-5}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x-6)& = & -12 \color{red}{-} (1+3x) \\\Leftrightarrow & 2x-12& = &-12-1-3x \\\Leftrightarrow & 2x \color{red}{-12} & = &-13 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-12} \color{blue}{+12} \color{blue}{+3x} & = &-13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+12} \\\Leftrightarrow & 2x+3x& = &-13+12 \\\Leftrightarrow & 5x& = &-1 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-1}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-5x+7)& = & 4 \color{red}{-} (13-3x) \\\Leftrightarrow & -10x+14& = &4-13+3x \\\Leftrightarrow & -10x \color{red}{+14} & = &-9 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{+14} \color{blue}{-14} \color{blue}{-3x} & = &-9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-14} \\\Leftrightarrow & -10x-3x& = &-9-14 \\\Leftrightarrow & -13x& = &-23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{23}{13} & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-3x+7)& = & -3 \color{red}{-} (15+x) \\\Leftrightarrow & -6x+14& = &-3-15-x \\\Leftrightarrow & -6x \color{red}{+14} & = &-18 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -6x+x& = &-18-14 \\\Leftrightarrow & -5x& = &-32 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-32}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{32}{5} & & \\ & V = \left\{ \frac{32}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (5x+4)& = & 2 \color{red}{+} (11+x) \\\Leftrightarrow & 10x+8& = &2+11+x \\\Leftrightarrow & 10x \color{red}{+8} & = &13 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 10x-x& = &13-8 \\\Leftrightarrow & 9x& = &5 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{5}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{5}{9} & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-5x+6)& = & -4 \color{red}{+} (-10+x) \\\Leftrightarrow & -30x+36& = &-4-10+x \\\Leftrightarrow & -30x \color{red}{+36} & = &-14 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & -30x-x& = &-14-36 \\\Leftrightarrow & -31x& = &-50 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-50}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{50}{31} & & \\ & V = \left\{ \frac{50}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x+1)& = & 12 \color{red}{-} (-13+2x) \\\Leftrightarrow & 3x+3& = &12+13-2x \\\Leftrightarrow & 3x \color{red}{+3} & = &25 \color{red}{-2x} \\\Leftrightarrow & 3x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &25 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & 3x+2x& = &25-3 \\\Leftrightarrow & 5x& = &22 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{22}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{22}{5} & & \\ & V = \left\{ \frac{22}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (5x+7)& = & 3 \color{red}{+} (-2-2x) \\\Leftrightarrow & 15x+21& = &3-2-2x \\\Leftrightarrow & 15x \color{red}{+21} & = &1 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 15x+2x& = &1-21 \\\Leftrightarrow & 17x& = &-20 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-20}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-20}{17} & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (6x+2)& = & 2 \color{red}{+} (13+x) \\\Leftrightarrow & 24x+8& = &2+13+x \\\Leftrightarrow & 24x \color{red}{+8} & = &15 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 24x-x& = &15-8 \\\Leftrightarrow & 23x& = &7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{7}{23} & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)