Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-3x+5)& = & -2 \color{red}{-} (-6+x) \\\Leftrightarrow & -6x+10& = &-2+6-x \\\Leftrightarrow & -6x \color{red}{+10} & = &4 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & -6x+x& = &4-10 \\\Leftrightarrow & -5x& = &-6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (3x-5)& = & 9 \color{red}{+} (-2+x) \\\Leftrightarrow & 12x-20& = &9-2+x \\\Leftrightarrow & 12x \color{red}{-20} & = &7 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+20} \\\Leftrightarrow & 12x-x& = &7+20 \\\Leftrightarrow & 11x& = &27 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{27}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{27}{11} & & \\ & V = \left\{ \frac{27}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-3x-4)& = & -4 \color{red}{+} (-6-2x) \\\Leftrightarrow & -9x-12& = &-4-6-2x \\\Leftrightarrow & -9x \color{red}{-12} & = &-10 \color{red}{-2x} \\\Leftrightarrow & -9x \color{red}{-12} \color{blue}{+12} \color{blue}{+2x} & = &-10 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+12} \\\Leftrightarrow & -9x+2x& = &-10+12 \\\Leftrightarrow & -7x& = &2 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{2}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (4x-2)& = & 13 \color{red}{+} (1+x) \\\Leftrightarrow & 20x-10& = &13+1+x \\\Leftrightarrow & 20x \color{red}{-10} & = &14 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 20x-x& = &14+10 \\\Leftrightarrow & 19x& = &24 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{24}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{24}{19} & & \\ & V = \left\{ \frac{24}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (x-6)& = & 13 \color{red}{-} (-7+x) \\\Leftrightarrow & 4x-24& = &13+7-x \\\Leftrightarrow & 4x \color{red}{-24} & = &20 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 4x+x& = &20+24 \\\Leftrightarrow & 5x& = &44 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{44}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{44}{5} & & \\ & V = \left\{ \frac{44}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (6x-6)& = & -14 \color{red}{+} (4+x) \\\Leftrightarrow & 30x-30& = &-14+4+x \\\Leftrightarrow & 30x \color{red}{-30} & = &-10 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &-10+30 \\\Leftrightarrow & 29x& = &20 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{20}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{20}{29} & & \\ & V = \left\{ \frac{20}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (5x-7)& = & -9 \color{red}{+} (-8+x) \\\Leftrightarrow & 30x-42& = &-9-8+x \\\Leftrightarrow & 30x \color{red}{-42} & = &-17 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 30x-x& = &-17+42 \\\Leftrightarrow & 29x& = &25 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{25}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{25}{29} & & \\ & V = \left\{ \frac{25}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (6x+2)& = & -11 \color{red}{+} (-3+x) \\\Leftrightarrow & 24x+8& = &-11-3+x \\\Leftrightarrow & 24x \color{red}{+8} & = &-14 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 24x-x& = &-14-8 \\\Leftrightarrow & 23x& = &-22 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-22}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x+3)& = & -11 \color{red}{+} (15+x) \\\Leftrightarrow & -8x+6& = &-11+15+x \\\Leftrightarrow & -8x \color{red}{+6} & = &4 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+6} \color{blue}{-6} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-6} \\\Leftrightarrow & -8x-x& = &4-6 \\\Leftrightarrow & -9x& = &-2 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-2}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (2x+4)& = & 6 \color{red}{+} (6+x) \\\Leftrightarrow & 4x+8& = &6+6+x \\\Leftrightarrow & 4x \color{red}{+8} & = &12 \color{red}{+x} \\\Leftrightarrow & 4x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &12 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 4x-x& = &12-8 \\\Leftrightarrow & 3x& = &4 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{4}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x+4)& = & -2 \color{red}{-} (11-5x) \\\Leftrightarrow & 36x+24& = &-2-11+5x \\\Leftrightarrow & 36x \color{red}{+24} & = &-13 \color{red}{+5x} \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &-13 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 36x-5x& = &-13-24 \\\Leftrightarrow & 31x& = &-37 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-37}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-37}{31} & & \\ & V = \left\{ \frac{-37}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-x+1)& = & 8 \color{red}{-} (11+x) \\\Leftrightarrow & -4x+4& = &8-11-x \\\Leftrightarrow & -4x \color{red}{+4} & = &-3 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{+4} \color{blue}{-4} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-4} \\\Leftrightarrow & -4x+x& = &-3-4 \\\Leftrightarrow & -3x& = &-7 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-7}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)