Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x-4)& = & -6 \color{red}{-} (-11-5x) \\\Leftrightarrow & 8x-8& = &-6+11+5x \\\Leftrightarrow & 8x \color{red}{-8} & = &5 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &5 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & 8x-5x& = &5+8 \\\Leftrightarrow & 3x& = &13 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{13}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{13}{3} & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-3x-4)& = & -7 \color{red}{+} (-7+x) \\\Leftrightarrow & -6x-8& = &-7-7+x \\\Leftrightarrow & -6x \color{red}{-8} & = &-14 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -6x-x& = &-14+8 \\\Leftrightarrow & -7x& = &-6 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-6}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+4)& = & -3 \color{red}{-} (6-2x) \\\Leftrightarrow & 15x+20& = &-3-6+2x \\\Leftrightarrow & 15x \color{red}{+20} & = &-9 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+20} \color{blue}{-20} \color{blue}{-2x} & = &-9 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-20} \\\Leftrightarrow & 15x-2x& = &-9-20 \\\Leftrightarrow & 13x& = &-29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-x+6)& = & -3 \color{red}{+} (11+4x) \\\Leftrightarrow & -3x+18& = &-3+11+4x \\\Leftrightarrow & -3x \color{red}{+18} & = &8 \color{red}{+4x} \\\Leftrightarrow & -3x \color{red}{+18} \color{blue}{-18} \color{blue}{-4x} & = &8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-18} \\\Leftrightarrow & -3x-4x& = &8-18 \\\Leftrightarrow & -7x& = &-10 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-10}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{10}{7} & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (2x+4)& = & 4 \color{red}{+} (5+3x) \\\Leftrightarrow & 8x+16& = &4+5+3x \\\Leftrightarrow & 8x \color{red}{+16} & = &9 \color{red}{+3x} \\\Leftrightarrow & 8x \color{red}{+16} \color{blue}{-16} \color{blue}{-3x} & = &9 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-16} \\\Leftrightarrow & 8x-3x& = &9-16 \\\Leftrightarrow & 5x& = &-7 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-7}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-7}{5} & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-5x-4)& = & 4 \color{red}{-} (4+x) \\\Leftrightarrow & -30x-24& = &4-4-x \\\Leftrightarrow & -30x \color{red}{-24} & = &0 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -30x+x& = &0+24 \\\Leftrightarrow & -29x& = &24 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{24}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-24}{29} & & \\ & V = \left\{ \frac{-24}{29} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (4x+7)& = & -10 \color{red}{+} (-15+x) \\\Leftrightarrow & 12x+21& = &-10-15+x \\\Leftrightarrow & 12x \color{red}{+21} & = &-25 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 12x-x& = &-25-21 \\\Leftrightarrow & 11x& = &-46 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-46}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-46}{11} & & \\ & V = \left\{ \frac{-46}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-7)& = & 12 \color{red}{+} (8+x) \\\Leftrightarrow & -20x-28& = &12+8+x \\\Leftrightarrow & -20x \color{red}{-28} & = &20 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -20x-x& = &20+28 \\\Leftrightarrow & -21x& = &48 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{48}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x+2)& = & 5 \color{red}{+} (-4+x) \\\Leftrightarrow & -10x+10& = &5-4+x \\\Leftrightarrow & -10x \color{red}{+10} & = &1 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & -10x-x& = &1-10 \\\Leftrightarrow & -11x& = &-9 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-9}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{9}{11} & & \\ & V = \left\{ \frac{9}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x+6)& = & 11 \color{red}{+} (-12+x) \\\Leftrightarrow & -2x+12& = &11-12+x \\\Leftrightarrow & -2x \color{red}{+12} & = &-1 \color{red}{+x} \\\Leftrightarrow & -2x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -2x-x& = &-1-12 \\\Leftrightarrow & -3x& = &-13 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-13}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{13}{3} & & \\ & V = \left\{ \frac{13}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (5x-1)& = & -1 \color{red}{-} (-14+3x) \\\Leftrightarrow & 20x-4& = &-1+14-3x \\\Leftrightarrow & 20x \color{red}{-4} & = &13 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{+3x} & = &13 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+4} \\\Leftrightarrow & 20x+3x& = &13+4 \\\Leftrightarrow & 23x& = &17 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{17}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{17}{23} & & \\ & V = \left\{ \frac{17}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x-1)& = & -12 \color{red}{-} (11+x) \\\Leftrightarrow & 24x-6& = &-12-11-x \\\Leftrightarrow & 24x \color{red}{-6} & = &-23 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 24x+x& = &-23+6 \\\Leftrightarrow & 25x& = &-17 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-17}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-17}{25} & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)