Vgln. eerste graad (reeks 3)

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Reeks met haakjes

1. \(5(-4x-4)=-14-(-10+3x)\)
2. \(2(5x+4)=-6+(14+x)\)
3. \(6(4x+7)=-4-(7+x)\)
4. \(3(5x+3)=8+(11+4x)\)
5. \(3(6x+2)=-2-(-13-5x)\)
6. \(3(6x-6)=-1-(9-5x)\)
7. \(6(-5x+4)=-13+(11+x)\)
8. \(5(x-5)=-2-(-6+x)\)
9. \(3(6x-7)=-4+(5+x)\)
10. \(6(3x+2)=7-(-3-5x)\)
11. \(2(4x-7)=9-(15+3x)\)
12. \(5(x+4)=-2-(-2+x)\)

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-4x-4)& = & -14 \color{red}{-} (-10+3x) \\\Leftrightarrow & -20x-20& = &-14+10-3x \\\Leftrightarrow & -20x \color{red}{-20} & = &-4 \color{red}{-3x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{+3x} & = &-4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+20} \\\Leftrightarrow & -20x+3x& = &-4+20 \\\Leftrightarrow & -17x& = &16 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{16}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-16}{17} & & \\ & V = \left\{ \frac{-16}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (5x+4)& = & -6 \color{red}{+} (14+x) \\\Leftrightarrow & 10x+8& = &-6+14+x \\\Leftrightarrow & 10x \color{red}{+8} & = &8 \color{red}{+x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{-8} \\\Leftrightarrow & 10x-x& = &8-8 \\\Leftrightarrow & 9x& = &0 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{0}{ \color{red}{9} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x+7)& = & -4 \color{red}{-} (7+x) \\\Leftrightarrow & 24x+42& = &-4-7-x \\\Leftrightarrow & 24x \color{red}{+42} & = &-11 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &-11 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & 24x+x& = &-11-42 \\\Leftrightarrow & 25x& = &-53 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-53}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-53}{25} & & \\ & V = \left\{ \frac{-53}{25} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x+3)& = & 8 \color{red}{+} (11+4x) \\\Leftrightarrow & 15x+9& = &8+11+4x \\\Leftrightarrow & 15x \color{red}{+9} & = &19 \color{red}{+4x} \\\Leftrightarrow & 15x \color{red}{+9} \color{blue}{-9} \color{blue}{-4x} & = &19 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-9} \\\Leftrightarrow & 15x-4x& = &19-9 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (6x+2)& = & -2 \color{red}{-} (-13-5x) \\\Leftrightarrow & 18x+6& = &-2+13+5x \\\Leftrightarrow & 18x \color{red}{+6} & = &11 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+6} \color{blue}{-6} \color{blue}{-5x} & = &11 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-6} \\\Leftrightarrow & 18x-5x& = &11-6 \\\Leftrightarrow & 13x& = &5 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{5}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{5}{13} & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{3} (6x-6)& = & -1 \color{red}{-} (9-5x) \\\Leftrightarrow & 18x-18& = &-1-9+5x \\\Leftrightarrow & 18x \color{red}{-18} & = &-10 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-5x} & = &-10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+18} \\\Leftrightarrow & 18x-5x& = &-10+18 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x+4)& = & -13 \color{red}{+} (11+x) \\\Leftrightarrow & -30x+24& = &-13+11+x \\\Leftrightarrow & -30x \color{red}{+24} & = &-2 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -30x-x& = &-2-24 \\\Leftrightarrow & -31x& = &-26 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-26}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{26}{31} & & \\ & V = \left\{ \frac{26}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (x-5)& = & -2 \color{red}{-} (-6+x) \\\Leftrightarrow & 5x-25& = &-2+6-x \\\Leftrightarrow & 5x \color{red}{-25} & = &4 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &4 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 5x+x& = &4+25 \\\Leftrightarrow & 6x& = &29 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{29}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{29}{6} & & \\ & V = \left\{ \frac{29}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x-7)& = & -4 \color{red}{+} (5+x) \\\Leftrightarrow & 18x-21& = &-4+5+x \\\Leftrightarrow & 18x \color{red}{-21} & = &1 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 18x-x& = &1+21 \\\Leftrightarrow & 17x& = &22 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{22}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{22}{17} & & \\ & V = \left\{ \frac{22}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (3x+2)& = & 7 \color{red}{-} (-3-5x) \\\Leftrightarrow & 18x+12& = &7+3+5x \\\Leftrightarrow & 18x \color{red}{+12} & = &10 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &10 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 18x-5x& = &10-12 \\\Leftrightarrow & 13x& = &-2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-2}{13} & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (4x-7)& = & 9 \color{red}{-} (15+3x) \\\Leftrightarrow & 8x-14& = &9-15-3x \\\Leftrightarrow & 8x \color{red}{-14} & = &-6 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-6 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & 8x+3x& = &-6+14 \\\Leftrightarrow & 11x& = &8 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{8}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{8}{11} & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (x+4)& = & -2 \color{red}{-} (-2+x) \\\Leftrightarrow & 5x+20& = &-2+2-x \\\Leftrightarrow & 5x \color{red}{+20} & = &0 \color{red}{-x} \\\Leftrightarrow & 5x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & 5x+x& = &0-20 \\\Leftrightarrow & 6x& = &-20 \\\Leftrightarrow & \frac{6x}{ \color{red}{6} }& = &\frac{-20}{ \color{red}{6} } \\\Leftrightarrow & x = \frac{-10}{3} & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)