Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (x+2)& = & -3 \color{red}{-} (8-2x) \\\Leftrightarrow & 3x+6& = &-3-8+2x \\\Leftrightarrow & 3x \color{red}{+6} & = &-11 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{+6} \color{blue}{-6} \color{blue}{-2x} & = &-11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-6} \\\Leftrightarrow & 3x-2x& = &-11-6 \\\Leftrightarrow & x& = &-17 \\ & V = \left\{ -17 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x+5)& = & -8 \color{red}{+} (7+3x) \\\Leftrightarrow & -4x+10& = &-8+7+3x \\\Leftrightarrow & -4x \color{red}{+10} & = &-1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &-1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & -4x-3x& = &-1-10 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-x-7)& = & -8 \color{red}{-} (-9+x) \\\Leftrightarrow & -4x-28& = &-8+9-x \\\Leftrightarrow & -4x \color{red}{-28} & = &1 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & -4x+x& = &1+28 \\\Leftrightarrow & -3x& = &29 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{29}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-29}{3} & & \\ & V = \left\{ \frac{-29}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (x-1)& = & -12 \color{red}{-} (-10+3x) \\\Leftrightarrow & 2x-2& = &-12+10-3x \\\Leftrightarrow & 2x \color{red}{-2} & = &-2 \color{red}{-3x} \\\Leftrightarrow & 2x \color{red}{-2} \color{blue}{+2} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+2} \\\Leftrightarrow & 2x+3x& = &-2+2 \\\Leftrightarrow & 5x& = &0 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{0}{ \color{red}{5} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (2x-1)& = & 10 \color{red}{-} (6+3x) \\\Leftrightarrow & 10x-5& = &10-6-3x \\\Leftrightarrow & 10x \color{red}{-5} & = &4 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{-5} \color{blue}{+5} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+5} \\\Leftrightarrow & 10x+3x& = &4+5 \\\Leftrightarrow & 13x& = &9 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{9}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (3x+5)& = & -5 \color{red}{-} (4+x) \\\Leftrightarrow & 12x+20& = &-5-4-x \\\Leftrightarrow & 12x \color{red}{+20} & = &-9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 12x+x& = &-9-20 \\\Leftrightarrow & 13x& = &-29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-4x-3)& = & 8 \color{red}{-} (-12+x) \\\Leftrightarrow & -20x-15& = &8+12-x \\\Leftrightarrow & -20x \color{red}{-15} & = &20 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -20x+x& = &20+15 \\\Leftrightarrow & -19x& = &35 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{35}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-35}{19} & & \\ & V = \left\{ \frac{-35}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (6x-5)& = & 9 \color{red}{+} (-5-5x) \\\Leftrightarrow & 18x-15& = &9-5-5x \\\Leftrightarrow & 18x \color{red}{-15} & = &4 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &4 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 18x+5x& = &4+15 \\\Leftrightarrow & 23x& = &19 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{19}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x+3)& = & -3 \color{red}{-} (4+x) \\\Leftrightarrow & 24x+18& = &-3-4-x \\\Leftrightarrow & 24x \color{red}{+18} & = &-7 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 24x+x& = &-7-18 \\\Leftrightarrow & 25x& = &-25 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-25}{ \color{red}{25} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x+5)& = & 5 \color{red}{+} (13+x) \\\Leftrightarrow & -30x+25& = &5+13+x \\\Leftrightarrow & -30x \color{red}{+25} & = &18 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &18-25 \\\Leftrightarrow & -31x& = &-7 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-7}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{7}{31} & & \\ & V = \left\{ \frac{7}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x+4)& = & 14 \color{red}{-} (-11+x) \\\Leftrightarrow & 6x+8& = &14+11-x \\\Leftrightarrow & 6x \color{red}{+8} & = &25 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &25 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & 6x+x& = &25-8 \\\Leftrightarrow & 7x& = &17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-3x-6)& = & 8 \color{red}{-} (-15+x) \\\Leftrightarrow & -6x-12& = &8+15-x \\\Leftrightarrow & -6x \color{red}{-12} & = &23 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -6x+x& = &23+12 \\\Leftrightarrow & -5x& = &35 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{35}{ \color{red}{-5} } \\\Leftrightarrow & x = -7 & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)