Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+5)& = & -4 \color{red}{-} (6+x) \\\Leftrightarrow & 10x+10& = &-4-6-x \\\Leftrightarrow & 10x \color{red}{+10} & = &-10 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 10x+x& = &-10-10 \\\Leftrightarrow & 11x& = &-20 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-20}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-20}{11} & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (2x+1)& = & 1 \color{red}{-} (-12-5x) \\\Leftrightarrow & 6x+3& = &1+12+5x \\\Leftrightarrow & 6x \color{red}{+3} & = &13 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & 6x-5x& = &13-3 \\\Leftrightarrow & x& = &10 \\ & V = \left\{ 10 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x-1)& = & -6 \color{red}{-} (2-5x) \\\Leftrightarrow & 6x-3& = &-6-2+5x \\\Leftrightarrow & 6x \color{red}{-3} & = &-8 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-3} \color{blue}{+3} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+3} \\\Leftrightarrow & 6x-5x& = &-8+3 \\\Leftrightarrow & x& = &-5 \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (2x+7)& = & 9 \color{red}{+} (-8+3x) \\\Leftrightarrow & 8x+28& = &9-8+3x \\\Leftrightarrow & 8x \color{red}{+28} & = &1 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-28} \\\Leftrightarrow & 8x-3x& = &1-28 \\\Leftrightarrow & 5x& = &-27 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-27}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-27}{5} & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-5x-2)& = & 5 \color{red}{-} (-15+x) \\\Leftrightarrow & -30x-12& = &5+15-x \\\Leftrightarrow & -30x \color{red}{-12} & = &20 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -30x+x& = &20+12 \\\Leftrightarrow & -29x& = &32 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{32}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-32}{29} & & \\ & V = \left\{ \frac{-32}{29} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x-5)& = & 5 \color{red}{-} (9+x) \\\Leftrightarrow & 6x-30& = &5-9-x \\\Leftrightarrow & 6x \color{red}{-30} & = &-4 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 6x+x& = &-4+30 \\\Leftrightarrow & 7x& = &26 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{26}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{26}{7} & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-x+4)& = & 15 \color{red}{+} (-15+3x) \\\Leftrightarrow & -5x+20& = &15-15+3x \\\Leftrightarrow & -5x \color{red}{+20} & = &0 \color{red}{+3x} \\\Leftrightarrow & -5x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &0 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -5x-3x& = &0-20 \\\Leftrightarrow & -8x& = &-20 \\\Leftrightarrow & \frac{-8x}{ \color{red}{-8} }& = &\frac{-20}{ \color{red}{-8} } \\\Leftrightarrow & x = \frac{5}{2} & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x-4)& = & -3 \color{red}{+} (11+x) \\\Leftrightarrow & 12x-24& = &-3+11+x \\\Leftrightarrow & 12x \color{red}{-24} & = &8 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & 12x-x& = &8+24 \\\Leftrightarrow & 11x& = &32 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{32}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{32}{11} & & \\ & V = \left\{ \frac{32}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-6x-7)& = & 4 \color{red}{-} (-8+x) \\\Leftrightarrow & -30x-35& = &4+8-x \\\Leftrightarrow & -30x \color{red}{-35} & = &12 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -30x+x& = &12+35 \\\Leftrightarrow & -29x& = &47 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{47}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-47}{29} & & \\ & V = \left\{ \frac{-47}{29} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-4x-3)& = & 2 \color{red}{-} (14+x) \\\Leftrightarrow & -8x-6& = &2-14-x \\\Leftrightarrow & -8x \color{red}{-6} & = &-12 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -8x+x& = &-12+6 \\\Leftrightarrow & -7x& = &-6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-3x-7)& = & -15 \color{red}{-} (6-2x) \\\Leftrightarrow & -15x-35& = &-15-6+2x \\\Leftrightarrow & -15x \color{red}{-35} & = &-21 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &-21 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & -15x-2x& = &-21+35 \\\Leftrightarrow & -17x& = &14 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{14}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-14}{17} & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (3x-6)& = & -3 \color{red}{-} (-6+2x) \\\Leftrightarrow & 9x-18& = &-3+6-2x \\\Leftrightarrow & 9x \color{red}{-18} & = &3 \color{red}{-2x} \\\Leftrightarrow & 9x \color{red}{-18} \color{blue}{+18} \color{blue}{+2x} & = &3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+18} \\\Leftrightarrow & 9x+2x& = &3+18 \\\Leftrightarrow & 11x& = &21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)