Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (3x+4)& = & 11 \color{red}{-} (-5-5x) \\\Leftrightarrow & 18x+24& = &11+5+5x \\\Leftrightarrow & 18x \color{red}{+24} & = &16 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+24} \color{blue}{-24} \color{blue}{-5x} & = &16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-24} \\\Leftrightarrow & 18x-5x& = &16-24 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (6x-3)& = & -11 \color{red}{-} (-9-5x) \\\Leftrightarrow & 18x-9& = &-11+9+5x \\\Leftrightarrow & 18x \color{red}{-9} & = &-2 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-9} \color{blue}{+9} \color{blue}{-5x} & = &-2 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+9} \\\Leftrightarrow & 18x-5x& = &-2+9 \\\Leftrightarrow & 13x& = &7 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{7}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (3x+6)& = & 9 \color{red}{-} (12+x) \\\Leftrightarrow & 18x+36& = &9-12-x \\\Leftrightarrow & 18x \color{red}{+36} & = &-3 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &-3 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 18x+x& = &-3-36 \\\Leftrightarrow & 19x& = &-39 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-39}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-39}{19} & & \\ & V = \left\{ \frac{-39}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (3x-1)& = & 9 \color{red}{-} (13+x) \\\Leftrightarrow & 9x-3& = &9-13-x \\\Leftrightarrow & 9x \color{red}{-3} & = &-4 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & 9x+x& = &-4+3 \\\Leftrightarrow & 10x& = &-1 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{-1}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{-1}{10} & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-6x+7)& = & 8 \color{red}{+} (14+x) \\\Leftrightarrow & -24x+28& = &8+14+x \\\Leftrightarrow & -24x \color{red}{+28} & = &22 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{+28} \color{blue}{-28} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{-28} \\\Leftrightarrow & -24x-x& = &22-28 \\\Leftrightarrow & -25x& = &-6 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{-6}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{6}{25} & & \\ & V = \left\{ \frac{6}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (4x-5)& = & -11 \color{red}{-} (-1-3x) \\\Leftrightarrow & 16x-20& = &-11+1+3x \\\Leftrightarrow & 16x \color{red}{-20} & = &-10 \color{red}{+3x} \\\Leftrightarrow & 16x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-10 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 16x-3x& = &-10+20 \\\Leftrightarrow & 13x& = &10 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{10}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{10}{13} & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (x+6)& = & 12 \color{red}{-} (-9+x) \\\Leftrightarrow & 3x+18& = &12+9-x \\\Leftrightarrow & 3x \color{red}{+18} & = &21 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &21 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 3x+x& = &21-18 \\\Leftrightarrow & 4x& = &3 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{3}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{3}{4} & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (x+7)& = & -3 \color{red}{+} (-12-5x) \\\Leftrightarrow & 6x+42& = &-3-12-5x \\\Leftrightarrow & 6x \color{red}{+42} & = &-15 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+42} \color{blue}{-42} \color{blue}{+5x} & = &-15 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-42} \\\Leftrightarrow & 6x+5x& = &-15-42 \\\Leftrightarrow & 11x& = &-57 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-57}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-57}{11} & & \\ & V = \left\{ \frac{-57}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (4x+5)& = & 3 \color{red}{-} (10+x) \\\Leftrightarrow & 12x+15& = &3-10-x \\\Leftrightarrow & 12x \color{red}{+15} & = &-7 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 12x+x& = &-7-15 \\\Leftrightarrow & 13x& = &-22 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-22}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (-x-4)& = & 8 \color{red}{+} (-4+x) \\\Leftrightarrow & -6x-24& = &8-4+x \\\Leftrightarrow & -6x \color{red}{-24} & = &4 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -6x-x& = &4+24 \\\Leftrightarrow & -7x& = &28 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{28}{ \color{red}{-7} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (3x-5)& = & 11 \color{red}{+} (-11-5x) \\\Leftrightarrow & 18x-30& = &11-11-5x \\\Leftrightarrow & 18x \color{red}{-30} & = &0 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &0 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & 18x+5x& = &0+30 \\\Leftrightarrow & 23x& = &30 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{30}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{30}{23} & & \\ & V = \left\{ \frac{30}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x-7)& = & -15 \color{red}{+} (10+x) \\\Leftrightarrow & 6x-21& = &-15+10+x \\\Leftrightarrow & 6x \color{red}{-21} & = &-5 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 6x-x& = &-5+21 \\\Leftrightarrow & 5x& = &16 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{16}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{16}{5} & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)