Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (4x-3)& = & 1 \color{red}{+} (6+x) \\\Leftrightarrow & 8x-6& = &1+6+x \\\Leftrightarrow & 8x \color{red}{-6} & = &7 \color{red}{+x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & 8x-x& = &7+6 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x+7)& = & -8 \color{red}{-} (-9+x) \\\Leftrightarrow & 18x+21& = &-8+9-x \\\Leftrightarrow & 18x \color{red}{+21} & = &1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 18x+x& = &1-21 \\\Leftrightarrow & 19x& = &-20 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-20}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-20}{19} & & \\ & V = \left\{ \frac{-20}{19} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (x+3)& = & 13 \color{red}{+} (8+4x) \\\Leftrightarrow & 5x+15& = &13+8+4x \\\Leftrightarrow & 5x \color{red}{+15} & = &21 \color{red}{+4x} \\\Leftrightarrow & 5x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &21 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & 5x-4x& = &21-15 \\\Leftrightarrow & x& = &6 \\ & V = \left\{ 6 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (5x+1)& = & -12 \color{red}{-} (-3+3x) \\\Leftrightarrow & 20x+4& = &-12+3-3x \\\Leftrightarrow & 20x \color{red}{+4} & = &-9 \color{red}{-3x} \\\Leftrightarrow & 20x \color{red}{+4} \color{blue}{-4} \color{blue}{+3x} & = &-9 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-4} \\\Leftrightarrow & 20x+3x& = &-9-4 \\\Leftrightarrow & 23x& = &-13 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-13}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-13}{23} & & \\ & V = \left\{ \frac{-13}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (3x+4)& = & -7 \color{red}{+} (-8+x) \\\Leftrightarrow & 18x+24& = &-7-8+x \\\Leftrightarrow & 18x \color{red}{+24} & = &-15 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 18x-x& = &-15-24 \\\Leftrightarrow & 17x& = &-39 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-39}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-39}{17} & & \\ & V = \left\{ \frac{-39}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x-2)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & -24x-12& = &8-4+x \\\Leftrightarrow & -24x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &4+12 \\\Leftrightarrow & -25x& = &16 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{16}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-16}{25} & & \\ & V = \left\{ \frac{-16}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x-7)& = & -13 \color{red}{+} (5+x) \\\Leftrightarrow & -8x-28& = &-13+5+x \\\Leftrightarrow & -8x \color{red}{-28} & = &-8 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -8x-x& = &-8+28 \\\Leftrightarrow & -9x& = &20 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{20}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-20}{9} & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (2x-7)& = & -13 \color{red}{-} (14-5x) \\\Leftrightarrow & 6x-21& = &-13-14+5x \\\Leftrightarrow & 6x \color{red}{-21} & = &-27 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &-27 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & 6x-5x& = &-27+21 \\\Leftrightarrow & x& = &-6 \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-x-2)& = & -7 \color{red}{-} (4-5x) \\\Leftrightarrow & -6x-12& = &-7-4+5x \\\Leftrightarrow & -6x \color{red}{-12} & = &-11 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &-11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -6x-5x& = &-11+12 \\\Leftrightarrow & -11x& = &1 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{1}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-2x+5)& = & -6 \color{red}{+} (11+3x) \\\Leftrightarrow & -8x+20& = &-6+11+3x \\\Leftrightarrow & -8x \color{red}{+20} & = &5 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{-3x} & = &5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-20} \\\Leftrightarrow & -8x-3x& = &5-20 \\\Leftrightarrow & -11x& = &-15 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-15}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{15}{11} & & \\ & V = \left\{ \frac{15}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x+1)& = & -8 \color{red}{-} (1+x) \\\Leftrightarrow & -8x+2& = &-8-1-x \\\Leftrightarrow & -8x \color{red}{+2} & = &-9 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -8x+x& = &-9-2 \\\Leftrightarrow & -7x& = &-11 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-11}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{11}{7} & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-4x-7)& = & -1 \color{red}{-} (11+x) \\\Leftrightarrow & -20x-35& = &-1-11-x \\\Leftrightarrow & -20x \color{red}{-35} & = &-12 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-35} \color{blue}{+35} \color{blue}{+x} & = &-12 \color{red}{-x} \color{blue}{+x} \color{blue}{+35} \\\Leftrightarrow & -20x+x& = &-12+35 \\\Leftrightarrow & -19x& = &23 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{23}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-23}{19} & & \\ & V = \left\{ \frac{-23}{19} \right\} & \\\end{align}\)