Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (6x+7)& = & -6 \color{red}{-} (2-5x) \\\Leftrightarrow & 18x+21& = &-6-2+5x \\\Leftrightarrow & 18x \color{red}{+21} & = &-8 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{+21} \color{blue}{-21} \color{blue}{-5x} & = &-8 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-21} \\\Leftrightarrow & 18x-5x& = &-8-21 \\\Leftrightarrow & 13x& = &-29 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-29}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-29}{13} & & \\ & V = \left\{ \frac{-29}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (3x-5)& = & 11 \color{red}{-} (-2+4x) \\\Leftrightarrow & 9x-15& = &11+2-4x \\\Leftrightarrow & 9x \color{red}{-15} & = &13 \color{red}{-4x} \\\Leftrightarrow & 9x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &13 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & 9x+4x& = &13+15 \\\Leftrightarrow & 13x& = &28 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{28}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{28}{13} & & \\ & V = \left\{ \frac{28}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-2x-2)& = & 9 \color{red}{+} (11+x) \\\Leftrightarrow & -6x-6& = &9+11+x \\\Leftrightarrow & -6x \color{red}{-6} & = &20 \color{red}{+x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &20 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -6x-x& = &20+6 \\\Leftrightarrow & -7x& = &26 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{26}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-26}{7} & & \\ & V = \left\{ \frac{-26}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x-4)& = & 5 \color{red}{+} (3+x) \\\Leftrightarrow & 18x-12& = &5+3+x \\\Leftrightarrow & 18x \color{red}{-12} & = &8 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 18x-x& = &8+12 \\\Leftrightarrow & 17x& = &20 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{20}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{20}{17} & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (x+3)& = & 10 \color{red}{-} (-12-5x) \\\Leftrightarrow & 3x+9& = &10+12+5x \\\Leftrightarrow & 3x \color{red}{+9} & = &22 \color{red}{+5x} \\\Leftrightarrow & 3x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &22 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 3x-5x& = &22-9 \\\Leftrightarrow & -2x& = &13 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{13}{ \color{red}{-2} } \\\Leftrightarrow & x = \frac{-13}{2} & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-4x-2)& = & 7 \color{red}{-} (-9-5x) \\\Leftrightarrow & -16x-8& = &7+9+5x \\\Leftrightarrow & -16x \color{red}{-8} & = &16 \color{red}{+5x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = &16 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & -16x-5x& = &16+8 \\\Leftrightarrow & -21x& = &24 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{24}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-6)& = & 9 \color{red}{+} (-1+x) \\\Leftrightarrow & 18x-36& = &9-1+x \\\Leftrightarrow & 18x \color{red}{-36} & = &8 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &8 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 18x-x& = &8+36 \\\Leftrightarrow & 17x& = &44 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{44}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{44}{17} & & \\ & V = \left\{ \frac{44}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (-4x-3)& = & -7 \color{red}{-} (-5+x) \\\Leftrightarrow & -20x-15& = &-7+5-x \\\Leftrightarrow & -20x \color{red}{-15} & = &-2 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & -20x+x& = &-2+15 \\\Leftrightarrow & -19x& = &13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x+3)& = & 11 \color{red}{+} (11-5x) \\\Leftrightarrow & 16x+12& = &11+11-5x \\\Leftrightarrow & 16x \color{red}{+12} & = &22 \color{red}{-5x} \\\Leftrightarrow & 16x \color{red}{+12} \color{blue}{-12} \color{blue}{+5x} & = &22 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-12} \\\Leftrightarrow & 16x+5x& = &22-12 \\\Leftrightarrow & 21x& = &10 \\\Leftrightarrow & \frac{21x}{ \color{red}{21} }& = &\frac{10}{ \color{red}{21} } \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{4} (-5x+4)& = & 1 \color{red}{+} (-2+x) \\\Leftrightarrow & -20x+16& = &1-2+x \\\Leftrightarrow & -20x \color{red}{+16} & = &-1 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+16} \color{blue}{-16} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-16} \\\Leftrightarrow & -20x-x& = &-1-16 \\\Leftrightarrow & -21x& = &-17 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-17}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{17}{21} & & \\ & V = \left\{ \frac{17}{21} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-3x+6)& = & -9 \color{red}{+} (4+x) \\\Leftrightarrow & -9x+18& = &-9+4+x \\\Leftrightarrow & -9x \color{red}{+18} & = &-5 \color{red}{+x} \\\Leftrightarrow & -9x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & -9x-x& = &-5-18 \\\Leftrightarrow & -10x& = &-23 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = &\frac{-23}{ \color{red}{-10} } \\\Leftrightarrow & x = \frac{23}{10} & & \\ & V = \left\{ \frac{23}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-5x+5)& = & 8 \color{red}{+} (-3+4x) \\\Leftrightarrow & -15x+15& = &8-3+4x \\\Leftrightarrow & -15x \color{red}{+15} & = &5 \color{red}{+4x} \\\Leftrightarrow & -15x \color{red}{+15} \color{blue}{-15} \color{blue}{-4x} & = &5 \color{red}{+4x} \color{blue}{-4x} \color{blue}{-15} \\\Leftrightarrow & -15x-4x& = &5-15 \\\Leftrightarrow & -19x& = &-10 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-10}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{10}{19} & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)