Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (4x-2)& = & -6 \color{red}{+} (-6+x) \\\Leftrightarrow & 24x-12& = &-6-6+x \\\Leftrightarrow & 24x \color{red}{-12} & = &-12 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 24x-x& = &-12+12 \\\Leftrightarrow & 23x& = &0 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{0}{ \color{red}{23} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (x-5)& = & -12 \color{red}{-} (-4+x) \\\Leftrightarrow & 3x-15& = &-12+4-x \\\Leftrightarrow & 3x \color{red}{-15} & = &-8 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-8 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 3x+x& = &-8+15 \\\Leftrightarrow & 4x& = &7 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{7}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{7}{4} & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (4x-4)& = & -1 \color{red}{-} (11+3x) \\\Leftrightarrow & 20x-20& = &-1-11-3x \\\Leftrightarrow & 20x \color{red}{-20} & = &-12 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-12 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & 20x+3x& = &-12+20 \\\Leftrightarrow & 23x& = &8 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{8}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{8}{23} & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x+4)& = & 3 \color{red}{+} (-11+x) \\\Leftrightarrow & 15x+12& = &3-11+x \\\Leftrightarrow & 15x \color{red}{+12} & = &-8 \color{red}{+x} \\\Leftrightarrow & 15x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 15x-x& = &-8-12 \\\Leftrightarrow & 14x& = &-20 \\\Leftrightarrow & \frac{14x}{ \color{red}{14} }& = &\frac{-20}{ \color{red}{14} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (5x+3)& = & -2 \color{red}{+} (-12-3x) \\\Leftrightarrow & 10x+6& = &-2-12-3x \\\Leftrightarrow & 10x \color{red}{+6} & = &-14 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & 10x+3x& = &-14-6 \\\Leftrightarrow & 13x& = &-20 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-20}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-20}{13} & & \\ & V = \left\{ \frac{-20}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (2x+7)& = & -14 \color{red}{-} (11+x) \\\Leftrightarrow & 8x+28& = &-14-11-x \\\Leftrightarrow & 8x \color{red}{+28} & = &-25 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-25 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & 8x+x& = &-25-28 \\\Leftrightarrow & 9x& = &-53 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-53}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-53}{9} & & \\ & V = \left\{ \frac{-53}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (6x+5)& = & -2 \color{red}{+} (11+x) \\\Leftrightarrow & 30x+25& = &-2+11+x \\\Leftrightarrow & 30x \color{red}{+25} & = &9 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 30x-x& = &9-25 \\\Leftrightarrow & 29x& = &-16 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-16}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-16}{29} & & \\ & V = \left\{ \frac{-16}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-x+1)& = & -2 \color{red}{-} (9-2x) \\\Leftrightarrow & -5x+5& = &-2-9+2x \\\Leftrightarrow & -5x \color{red}{+5} & = &-11 \color{red}{+2x} \\\Leftrightarrow & -5x \color{red}{+5} \color{blue}{-5} \color{blue}{-2x} & = &-11 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-5} \\\Leftrightarrow & -5x-2x& = &-11-5 \\\Leftrightarrow & -7x& = &-16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-4x+4)& = & 12 \color{red}{+} (-8+x) \\\Leftrightarrow & -8x+8& = &12-8+x \\\Leftrightarrow & -8x \color{red}{+8} & = &4 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & -8x-x& = &4-8 \\\Leftrightarrow & -9x& = &-4 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-4}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-x-1)& = & 13 \color{red}{+} (-5+4x) \\\Leftrightarrow & -5x-5& = &13-5+4x \\\Leftrightarrow & -5x \color{red}{-5} & = &8 \color{red}{+4x} \\\Leftrightarrow & -5x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &8 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -5x-4x& = &8+5 \\\Leftrightarrow & -9x& = &13 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{13}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x+5)& = & -1 \color{red}{+} (-12+x) \\\Leftrightarrow & 6x+10& = &-1-12+x \\\Leftrightarrow & 6x \color{red}{+10} & = &-13 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+10} \color{blue}{-10} \color{blue}{-x} & = &-13 \color{red}{+x} \color{blue}{-x} \color{blue}{-10} \\\Leftrightarrow & 6x-x& = &-13-10 \\\Leftrightarrow & 5x& = &-23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-23}{5} & & \\ & V = \left\{ \frac{-23}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x-7)& = & -2 \color{red}{-} (-14+x) \\\Leftrightarrow & 5x-35& = &-2+14-x \\\Leftrightarrow & 5x \color{red}{-35} & = &12 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & 5x+x& = &12+35 \\\Leftrightarrow & 6x& = &47 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{47}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{47}{6} & & \\ & V = \left\{ \frac{47}{6} \right\} & \\\end{align}\)