Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x+1)& = & 15 \color{red}{+} (-12-5x) \\\Leftrightarrow & -18x+3& = &15-12-5x \\\Leftrightarrow & -18x \color{red}{+3} & = &3 \color{red}{-5x} \\\Leftrightarrow & -18x \color{red}{+3} \color{blue}{-3} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-3} \\\Leftrightarrow & -18x+5x& = &3-3 \\\Leftrightarrow & -13x& = &0 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{0}{ \color{red}{-13} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (6x+5)& = & 2 \color{red}{-} (6+x) \\\Leftrightarrow & 36x+30& = &2-6-x \\\Leftrightarrow & 36x \color{red}{+30} & = &-4 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & 36x+x& = &-4-30 \\\Leftrightarrow & 37x& = &-34 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-34}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-34}{37} & & \\ & V = \left\{ \frac{-34}{37} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (2x-3)& = & -4 \color{red}{-} (3-3x) \\\Leftrightarrow & 4x-6& = &-4-3+3x \\\Leftrightarrow & 4x \color{red}{-6} & = &-7 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & 4x-3x& = &-7+6 \\\Leftrightarrow & x& = &-1 \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-4x+1)& = & -4 \color{red}{+} (-14+3x) \\\Leftrightarrow & -16x+4& = &-4-14+3x \\\Leftrightarrow & -16x \color{red}{+4} & = &-18 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{+4} \color{blue}{-4} \color{blue}{-3x} & = &-18 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-4} \\\Leftrightarrow & -16x-3x& = &-18-4 \\\Leftrightarrow & -19x& = &-22 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-22}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{22}{19} & & \\ & V = \left\{ \frac{22}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+3)& = & 13 \color{red}{-} (13+x) \\\Leftrightarrow & 6x+18& = &13-13-x \\\Leftrightarrow & 6x \color{red}{+18} & = &0 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 6x+x& = &0-18 \\\Leftrightarrow & 7x& = &-18 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-18}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (2x-4)& = & -13 \color{red}{+} (10+3x) \\\Leftrightarrow & 10x-20& = &-13+10+3x \\\Leftrightarrow & 10x \color{red}{-20} & = &-3 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-3 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 10x-3x& = &-3+20 \\\Leftrightarrow & 7x& = &17 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{17}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{17}{7} & & \\ & V = \left\{ \frac{17}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-6x+6)& = & -11 \color{red}{-} (-14+x) \\\Leftrightarrow & -30x+30& = &-11+14-x \\\Leftrightarrow & -30x \color{red}{+30} & = &3 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+30} \color{blue}{-30} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{-30} \\\Leftrightarrow & -30x+x& = &3-30 \\\Leftrightarrow & -29x& = &-27 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-27}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{27}{29} & & \\ & V = \left\{ \frac{27}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (2x+3)& = & 3 \color{red}{+} (11+x) \\\Leftrightarrow & 12x+18& = &3+11+x \\\Leftrightarrow & 12x \color{red}{+18} & = &14 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 12x-x& = &14-18 \\\Leftrightarrow & 11x& = &-4 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-4}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-4}{11} & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (6x+4)& = & -11 \color{red}{-} (-10+x) \\\Leftrightarrow & 18x+12& = &-11+10-x \\\Leftrightarrow & 18x \color{red}{+12} & = &-1 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-1 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 18x+x& = &-1-12 \\\Leftrightarrow & 19x& = &-13 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-13}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+7)& = & -7 \color{red}{+} (8-2x) \\\Leftrightarrow & 15x+21& = &-7+8-2x \\\Leftrightarrow & 15x \color{red}{+21} & = &1 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{+2x} & = &1 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-21} \\\Leftrightarrow & 15x+2x& = &1-21 \\\Leftrightarrow & 17x& = &-20 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-20}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-20}{17} & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{5} (6x-6)& = & 2 \color{red}{+} (-14+x) \\\Leftrightarrow & 30x-30& = &2-14+x \\\Leftrightarrow & 30x \color{red}{-30} & = &-12 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &-12 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & 30x-x& = &-12+30 \\\Leftrightarrow & 29x& = &18 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{18}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{18}{29} & & \\ & V = \left\{ \frac{18}{29} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (3x-7)& = & 5 \color{red}{-} (-4+x) \\\Leftrightarrow & 12x-28& = &5+4-x \\\Leftrightarrow & 12x \color{red}{-28} & = &9 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-28} \color{blue}{+28} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{+28} \\\Leftrightarrow & 12x+x& = &9+28 \\\Leftrightarrow & 13x& = &37 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{37}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{37}{13} & & \\ & V = \left\{ \frac{37}{13} \right\} & \\\end{align}\)