Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-6x+5)& = & -6 \color{red}{+} (15+x) \\\Leftrightarrow & -30x+25& = &-6+15+x \\\Leftrightarrow & -30x \color{red}{+25} & = &9 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &9-25 \\\Leftrightarrow & -31x& = &-16 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-16}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{16}{31} & & \\ & V = \left\{ \frac{16}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (4x+3)& = & 10 \color{red}{-} (-14+x) \\\Leftrightarrow & 24x+18& = &10+14-x \\\Leftrightarrow & 24x \color{red}{+18} & = &24 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 24x+x& = &24-18 \\\Leftrightarrow & 25x& = &6 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{6}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{6}{25} & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (2x-7)& = & 7 \color{red}{+} (1-5x) \\\Leftrightarrow & 6x-21& = &7+1-5x \\\Leftrightarrow & 6x \color{red}{-21} & = &8 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{+5x} & = &8 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+21} \\\Leftrightarrow & 6x+5x& = &8+21 \\\Leftrightarrow & 11x& = &29 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{29}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{29}{11} & & \\ & V = \left\{ \frac{29}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (6x-1)& = & -9 \color{red}{+} (12+x) \\\Leftrightarrow & 24x-4& = &-9+12+x \\\Leftrightarrow & 24x \color{red}{-4} & = &3 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-4} \color{blue}{+4} \color{blue}{-x} & = &3 \color{red}{+x} \color{blue}{-x} \color{blue}{+4} \\\Leftrightarrow & 24x-x& = &3+4 \\\Leftrightarrow & 23x& = &7 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{7}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{7}{23} & & \\ & V = \left\{ \frac{7}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x+4)& = & -10 \color{red}{+} (-8+x) \\\Leftrightarrow & -12x+12& = &-10-8+x \\\Leftrightarrow & -12x \color{red}{+12} & = &-18 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -12x-x& = &-18-12 \\\Leftrightarrow & -13x& = &-30 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-30}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{30}{13} & & \\ & V = \left\{ \frac{30}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x+1)& = & -2 \color{red}{+} (-12-3x) \\\Leftrightarrow & 10x+5& = &-2-12-3x \\\Leftrightarrow & 10x \color{red}{+5} & = &-14 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+5} \color{blue}{-5} \color{blue}{+3x} & = &-14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-5} \\\Leftrightarrow & 10x+3x& = &-14-5 \\\Leftrightarrow & 13x& = &-19 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-19}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-19}{13} & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-3)& = & 5 \color{red}{+} (5-5x) \\\Leftrightarrow & 18x-9& = &5+5-5x \\\Leftrightarrow & 18x \color{red}{-9} & = &10 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{+5x} & = &10 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+9} \\\Leftrightarrow & 18x+5x& = &10+9 \\\Leftrightarrow & 23x& = &19 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{19}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{19}{23} & & \\ & V = \left\{ \frac{19}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x-4)& = & -6 \color{red}{-} (-4+x) \\\Leftrightarrow & -24x-24& = &-6+4-x \\\Leftrightarrow & -24x \color{red}{-24} & = &-2 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & -24x+x& = &-2+24 \\\Leftrightarrow & -23x& = &22 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{22}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-22}{23} & & \\ & V = \left\{ \frac{-22}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (-6x+7)& = & 7 \color{red}{+} (6-5x) \\\Leftrightarrow & -36x+42& = &7+6-5x \\\Leftrightarrow & -36x \color{red}{+42} & = &13 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &13 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & -36x+5x& = &13-42 \\\Leftrightarrow & -31x& = &-29 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-29}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{29}{31} & & \\ & V = \left\{ \frac{29}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-4x-7)& = & -4 \color{red}{+} (-15+3x) \\\Leftrightarrow & -16x-28& = &-4-15+3x \\\Leftrightarrow & -16x \color{red}{-28} & = &-19 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &-19 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & -16x-3x& = &-19+28 \\\Leftrightarrow & -19x& = &9 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{9}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-9}{19} & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-4x+6)& = & -1 \color{red}{-} (-2+x) \\\Leftrightarrow & -12x+18& = &-1+2-x \\\Leftrightarrow & -12x \color{red}{+18} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -12x+x& = &1-18 \\\Leftrightarrow & -11x& = &-17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (6x-6)& = & 7 \color{red}{+} (-2+x) \\\Leftrightarrow & 18x-18& = &7-2+x \\\Leftrightarrow & 18x \color{red}{-18} & = &5 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &5+18 \\\Leftrightarrow & 17x& = &23 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{23}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{23}{17} & & \\ & V = \left\{ \frac{23}{17} \right\} & \\\end{align}\)