Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (4x-6)& = & -2 \color{red}{-} (-6+x) \\\Leftrightarrow & 16x-24& = &-2+6-x \\\Leftrightarrow & 16x \color{red}{-24} & = &4 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 16x+x& = &4+24 \\\Leftrightarrow & 17x& = &28 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{28}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{28}{17} & & \\ & V = \left\{ \frac{28}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x+5)& = & -14 \color{red}{+} (-10-3x) \\\Leftrightarrow & -4x+20& = &-14-10-3x \\\Leftrightarrow & -4x \color{red}{+20} & = &-24 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &-24 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & -4x+3x& = &-24-20 \\\Leftrightarrow & -x& = &-44 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-44}{ \color{red}{-1} } \\\Leftrightarrow & x = 44 & & \\ & V = \left\{ 44 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x-6)& = & 6 \color{red}{+} (9+x) \\\Leftrightarrow & 18x-36& = &6+9+x \\\Leftrightarrow & 18x \color{red}{-36} & = &15 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 18x-x& = &15+36 \\\Leftrightarrow & 17x& = &51 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{51}{ \color{red}{17} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (2x-2)& = & 3 \color{red}{-} (-7-3x) \\\Leftrightarrow & 4x-4& = &3+7+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &10 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &10+4 \\\Leftrightarrow & x& = &14 \\ & V = \left\{ 14 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-x-4)& = & -5 \color{red}{+} (-5+x) \\\Leftrightarrow & -4x-16& = &-5-5+x \\\Leftrightarrow & -4x \color{red}{-16} & = &-10 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -4x-x& = &-10+16 \\\Leftrightarrow & -5x& = &6 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{6}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-6}{5} & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-x-4)& = & -1 \color{red}{+} (-7+x) \\\Leftrightarrow & -6x-24& = &-1-7+x \\\Leftrightarrow & -6x \color{red}{-24} & = &-8 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -6x-x& = &-8+24 \\\Leftrightarrow & -7x& = &16 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{16}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-16}{7} & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x+5)& = & 2 \color{red}{-} (-1+x) \\\Leftrightarrow & -8x+20& = &2+1-x \\\Leftrightarrow & -8x \color{red}{+20} & = &3 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -8x+x& = &3-20 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-4x+1)& = & -6 \color{red}{-} (7-3x) \\\Leftrightarrow & -16x+4& = &-6-7+3x \\\Leftrightarrow & -16x \color{red}{+4} & = &-13 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -16x-3x& = &-13-4 \\\Leftrightarrow & -19x& = &-17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-3x-5)& = & -9 \color{red}{-} (8+4x) \\\Leftrightarrow & -15x-25& = &-9-8-4x \\\Leftrightarrow & -15x \color{red}{-25} & = &-17 \color{red}{-4x} \\\Leftrightarrow & -15x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = &-17 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & -15x+4x& = &-17+25 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-2x-4)& = & 10 \color{red}{+} (3+x) \\\Leftrightarrow & -4x-8& = &10+3+x \\\Leftrightarrow & -4x \color{red}{-8} & = &13 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+8} \\\Leftrightarrow & -4x-x& = &13+8 \\\Leftrightarrow & -5x& = &21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (5x+1)& = & 10 \color{red}{-} (9+x) \\\Leftrightarrow & 30x+6& = &10-9-x \\\Leftrightarrow & 30x \color{red}{+6} & = &1 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 30x+x& = &1-6 \\\Leftrightarrow & 31x& = &-5 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-5}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-5}{31} & & \\ & V = \left\{ \frac{-5}{31} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x+1)& = & -2 \color{red}{+} (-4-5x) \\\Leftrightarrow & 18x+3& = &-2-4-5x \\\Leftrightarrow & 18x \color{red}{+3} & = &-6 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &-6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & 18x+5x& = &-6-3 \\\Leftrightarrow & 23x& = &-9 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-9}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-9}{23} & & \\ & V = \left\{ \frac{-9}{23} \right\} & \\\end{align}\)