Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x-5)& = & -12 \color{red}{-} (1-3x) \\\Leftrightarrow & 10x-10& = &-12-1+3x \\\Leftrightarrow & 10x \color{red}{-10} & = &-13 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &-13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & 10x-3x& = &-13+10 \\\Leftrightarrow & 7x& = &-3 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-3}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-3}{7} & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x+3)& = & -1 \color{red}{-} (9+x) \\\Leftrightarrow & -6x+9& = &-1-9-x \\\Leftrightarrow & -6x \color{red}{+9} & = &-10 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -6x+x& = &-10-9 \\\Leftrightarrow & -5x& = &-19 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-19}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{19}{5} & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x+4)& = & 6 \color{red}{-} (-3-5x) \\\Leftrightarrow & 6x+8& = &6+3+5x \\\Leftrightarrow & 6x \color{red}{+8} & = &9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+8} \color{blue}{-8} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-8} \\\Leftrightarrow & 6x-5x& = &9-8 \\\Leftrightarrow & x& = &1 \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (3x+7)& = & -10 \color{red}{+} (-7+x) \\\Leftrightarrow & 18x+42& = &-10-7+x \\\Leftrightarrow & 18x \color{red}{+42} & = &-17 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+42} \color{blue}{-42} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-42} \\\Leftrightarrow & 18x-x& = &-17-42 \\\Leftrightarrow & 17x& = &-59 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-59}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-59}{17} & & \\ & V = \left\{ \frac{-59}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x+6)& = & 7 \color{red}{-} (-13-5x) \\\Leftrightarrow & 6x+18& = &7+13+5x \\\Leftrightarrow & 6x \color{red}{+18} & = &20 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-5x} & = &20 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-18} \\\Leftrightarrow & 6x-5x& = &20-18 \\\Leftrightarrow & x& = &2 \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x+3)& = & -8 \color{red}{-} (-3-3x) \\\Leftrightarrow & -4x+12& = &-8+3+3x \\\Leftrightarrow & -4x \color{red}{+12} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -4x-3x& = &-5-12 \\\Leftrightarrow & -7x& = &-17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (6x+5)& = & -7 \color{red}{+} (15+x) \\\Leftrightarrow & 24x+20& = &-7+15+x \\\Leftrightarrow & 24x \color{red}{+20} & = &8 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+20} \color{blue}{-20} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-20} \\\Leftrightarrow & 24x-x& = &8-20 \\\Leftrightarrow & 23x& = &-12 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-12}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-12}{23} & & \\ & V = \left\{ \frac{-12}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-6x+7)& = & -13 \color{red}{+} (8+x) \\\Leftrightarrow & -12x+14& = &-13+8+x \\\Leftrightarrow & -12x \color{red}{+14} & = &-5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -12x-x& = &-5-14 \\\Leftrightarrow & -13x& = &-19 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-19}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{19}{13} & & \\ & V = \left\{ \frac{19}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x-5)& = & -2 \color{red}{+} (3-5x) \\\Leftrightarrow & 18x-15& = &-2+3-5x \\\Leftrightarrow & 18x \color{red}{-15} & = &1 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & 18x+5x& = &1+15 \\\Leftrightarrow & 23x& = &16 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{16}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (4x-7)& = & 5 \color{red}{+} (8+x) \\\Leftrightarrow & 24x-42& = &5+8+x \\\Leftrightarrow & 24x \color{red}{-42} & = &13 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &13 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 24x-x& = &13+42 \\\Leftrightarrow & 23x& = &55 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{55}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{55}{23} & & \\ & V = \left\{ \frac{55}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (x+3)& = & -8 \color{red}{-} (6+x) \\\Leftrightarrow & 2x+6& = &-8-6-x \\\Leftrightarrow & 2x \color{red}{+6} & = &-14 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 2x+x& = &-14-6 \\\Leftrightarrow & 3x& = &-20 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-20}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{-20}{3} & & \\ & V = \left\{ \frac{-20}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (-2x-2)& = & 9 \color{red}{-} (8-3x) \\\Leftrightarrow & -10x-10& = &9-8+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &1 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &1+10 \\\Leftrightarrow & -13x& = &11 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{11}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-11}{13} & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)