Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (5x-5)& = & -2 \color{red}{+} (2+x) \\\Leftrightarrow & 30x-30& = &-2+2+x \\\Leftrightarrow & 30x \color{red}{-30} & = &0 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &0 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &0+30 \\\Leftrightarrow & 29x& = &30 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{30}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{30}{29} & & \\ & V = \left\{ \frac{30}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-2)& = & -3 \color{red}{+} (-2+3x) \\\Leftrightarrow & -10x-4& = &-3-2+3x \\\Leftrightarrow & -10x \color{red}{-4} & = &-5 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-5 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & -10x-3x& = &-5+4 \\\Leftrightarrow & -13x& = &-1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-5x+3)& = & -13 \color{red}{+} (-12+x) \\\Leftrightarrow & -20x+12& = &-13-12+x \\\Leftrightarrow & -20x \color{red}{+12} & = &-25 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-25 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -20x-x& = &-25-12 \\\Leftrightarrow & -21x& = &-37 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-37}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{37}{21} & & \\ & V = \left\{ \frac{37}{21} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (5x-6)& = & 3 \color{red}{-} (-14+x) \\\Leftrightarrow & 15x-18& = &3+14-x \\\Leftrightarrow & 15x \color{red}{-18} & = &17 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &17 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 15x+x& = &17+18 \\\Leftrightarrow & 16x& = &35 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{35}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{35}{16} & & \\ & V = \left\{ \frac{35}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (2x+3)& = & 3 \color{red}{-} (-6-5x) \\\Leftrightarrow & 6x+9& = &3+6+5x \\\Leftrightarrow & 6x \color{red}{+9} & = &9 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{-5x} & = &9 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-9} \\\Leftrightarrow & 6x-5x& = &9-9 \\\Leftrightarrow & x& = &0 \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (-6x-1)& = & 13 \color{red}{+} (12+x) \\\Leftrightarrow & -12x-2& = &13+12+x \\\Leftrightarrow & -12x \color{red}{-2} & = &25 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -12x-x& = &25+2 \\\Leftrightarrow & -13x& = &27 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{27}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-27}{13} & & \\ & V = \left\{ \frac{-27}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (3x-6)& = & 6 \color{red}{-} (-6+x) \\\Leftrightarrow & 15x-30& = &6+6-x \\\Leftrightarrow & 15x \color{red}{-30} & = &12 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 15x+x& = &12+30 \\\Leftrightarrow & 16x& = &42 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{42}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{21}{8} & & \\ & V = \left\{ \frac{21}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x-1)& = & -15 \color{red}{+} (-5-2x) \\\Leftrightarrow & -15x-3& = &-15-5-2x \\\Leftrightarrow & -15x \color{red}{-3} & = &-20 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{-3} \color{blue}{+3} \color{blue}{+2x} & = &-20 \color{red}{-2x} \color{blue}{+2x} \color{blue}{+3} \\\Leftrightarrow & -15x+2x& = &-20+3 \\\Leftrightarrow & -13x& = &-17 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-17}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{17}{13} & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x+4)& = & 14 \color{red}{+} (-15+x) \\\Leftrightarrow & 6x+12& = &14-15+x \\\Leftrightarrow & 6x \color{red}{+12} & = &-1 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & 6x-x& = &-1-12 \\\Leftrightarrow & 5x& = &-13 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-13}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-13}{5} & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-5x+6)& = & -2 \color{red}{+} (9+3x) \\\Leftrightarrow & -25x+30& = &-2+9+3x \\\Leftrightarrow & -25x \color{red}{+30} & = &7 \color{red}{+3x} \\\Leftrightarrow & -25x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & -25x-3x& = &7-30 \\\Leftrightarrow & -28x& = &-23 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = &\frac{-23}{ \color{red}{-28} } \\\Leftrightarrow & x = \frac{23}{28} & & \\ & V = \left\{ \frac{23}{28} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (4x+2)& = & 7 \color{red}{-} (-7+x) \\\Leftrightarrow & 12x+6& = &7+7-x \\\Leftrightarrow & 12x \color{red}{+6} & = &14 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & 12x+x& = &14-6 \\\Leftrightarrow & 13x& = &8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{8}{13} & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-3x-7)& = & 12 \color{red}{+} (10+x) \\\Leftrightarrow & -12x-28& = &12+10+x \\\Leftrightarrow & -12x \color{red}{-28} & = &22 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-28} \color{blue}{+28} \color{blue}{-x} & = &22 \color{red}{+x} \color{blue}{-x} \color{blue}{+28} \\\Leftrightarrow & -12x-x& = &22+28 \\\Leftrightarrow & -13x& = &50 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{50}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-50}{13} & & \\ & V = \left\{ \frac{-50}{13} \right\} & \\\end{align}\)