Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (5x-3)& = & 4 \color{red}{+} (-15+x) \\\Leftrightarrow & 20x-12& = &4-15+x \\\Leftrightarrow & 20x \color{red}{-12} & = &-11 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 20x-x& = &-11+12 \\\Leftrightarrow & 19x& = &1 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{1}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{1}{19} & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (x+5)& = & -12 \color{red}{-} (2+x) \\\Leftrightarrow & 6x+30& = &-12-2-x \\\Leftrightarrow & 6x \color{red}{+30} & = &-14 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-14 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 6x+x& = &-14-30 \\\Leftrightarrow & 7x& = &-44 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-44}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-44}{7} & & \\ & V = \left\{ \frac{-44}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (-6x+3)& = & -11 \color{red}{+} (-15+x) \\\Leftrightarrow & -18x+9& = &-11-15+x \\\Leftrightarrow & -18x \color{red}{+9} & = &-26 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &-26 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & -18x-x& = &-26-9 \\\Leftrightarrow & -19x& = &-35 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-35}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{35}{19} & & \\ & V = \left\{ \frac{35}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-3x+7)& = & -4 \color{red}{-} (14+x) \\\Leftrightarrow & -12x+28& = &-4-14-x \\\Leftrightarrow & -12x \color{red}{+28} & = &-18 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+28} \color{blue}{-28} \color{blue}{+x} & = &-18 \color{red}{-x} \color{blue}{+x} \color{blue}{-28} \\\Leftrightarrow & -12x+x& = &-18-28 \\\Leftrightarrow & -11x& = &-46 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-46}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{46}{11} & & \\ & V = \left\{ \frac{46}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (3x-5)& = & 6 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x-20& = &6+7-x \\\Leftrightarrow & 12x \color{red}{-20} & = &13 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-20} \color{blue}{+20} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+20} \\\Leftrightarrow & 12x+x& = &13+20 \\\Leftrightarrow & 13x& = &33 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{33}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{33}{13} & & \\ & V = \left\{ \frac{33}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x-6)& = & -12 \color{red}{+} (11+x) \\\Leftrightarrow & -12x-24& = &-12+11+x \\\Leftrightarrow & -12x \color{red}{-24} & = &-1 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -12x-x& = &-1+24 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (3x-2)& = & 10 \color{red}{-} (9+x) \\\Leftrightarrow & 18x-12& = &10-9-x \\\Leftrightarrow & 18x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 18x+x& = &1+12 \\\Leftrightarrow & 19x& = &13 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{13}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (-3x-2)& = & -3 \color{red}{-} (-12-5x) \\\Leftrightarrow & -6x-4& = &-3+12+5x \\\Leftrightarrow & -6x \color{red}{-4} & = &9 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & -6x-5x& = &9+4 \\\Leftrightarrow & -11x& = &13 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{13}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-x-7)& = & 7 \color{red}{-} (14+3x) \\\Leftrightarrow & -2x-14& = &7-14-3x \\\Leftrightarrow & -2x \color{red}{-14} & = &-7 \color{red}{-3x} \\\Leftrightarrow & -2x \color{red}{-14} \color{blue}{+14} \color{blue}{+3x} & = &-7 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+14} \\\Leftrightarrow & -2x+3x& = &-7+14 \\\Leftrightarrow & x& = &7 \\ & V = \left\{ 7 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x+6)& = & -13 \color{red}{-} (-1-5x) \\\Leftrightarrow & 8x+12& = &-13+1+5x \\\Leftrightarrow & 8x \color{red}{+12} & = &-12 \color{red}{+5x} \\\Leftrightarrow & 8x \color{red}{+12} \color{blue}{-12} \color{blue}{-5x} & = &-12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-12} \\\Leftrightarrow & 8x-5x& = &-12-12 \\\Leftrightarrow & 3x& = &-24 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{-24}{ \color{red}{3} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (-5x-4)& = & 10 \color{red}{+} (-7-4x) \\\Leftrightarrow & -25x-20& = &10-7-4x \\\Leftrightarrow & -25x \color{red}{-20} & = &3 \color{red}{-4x} \\\Leftrightarrow & -25x \color{red}{-20} \color{blue}{+20} \color{blue}{+4x} & = &3 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+20} \\\Leftrightarrow & -25x+4x& = &3+20 \\\Leftrightarrow & -21x& = &23 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{23}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{-23}{21} & & \\ & V = \left\{ \frac{-23}{21} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (-6x-3)& = & 9 \color{red}{+} (-8+x) \\\Leftrightarrow & -36x-18& = &9-8+x \\\Leftrightarrow & -36x \color{red}{-18} & = &1 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &1 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -36x-x& = &1+18 \\\Leftrightarrow & -37x& = &19 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{19}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-19}{37} & & \\ & V = \left\{ \frac{-19}{37} \right\} & \\\end{align}\)