Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-4x+2)& = & -12 \color{red}{+} (8+x) \\\Leftrightarrow & -8x+4& = &-12+8+x \\\Leftrightarrow & -8x \color{red}{+4} & = &-4 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &-4 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -8x-x& = &-4-4 \\\Leftrightarrow & -9x& = &-8 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-8}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-1)& = & -12 \color{red}{-} (11+x) \\\Leftrightarrow & -10x-2& = &-12-11-x \\\Leftrightarrow & -10x \color{red}{-2} & = &-23 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -10x+x& = &-23+2 \\\Leftrightarrow & -9x& = &-21 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{-21}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (4x-7)& = & -8 \color{red}{+} (15+x) \\\Leftrightarrow & 24x-42& = &-8+15+x \\\Leftrightarrow & 24x \color{red}{-42} & = &7 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & 24x-x& = &7+42 \\\Leftrightarrow & 23x& = &49 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{49}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{49}{23} & & \\ & V = \left\{ \frac{49}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{2} (4x-3)& = & -14 \color{red}{-} (3+3x) \\\Leftrightarrow & 8x-6& = &-14-3-3x \\\Leftrightarrow & 8x \color{red}{-6} & = &-17 \color{red}{-3x} \\\Leftrightarrow & 8x \color{red}{-6} \color{blue}{+6} \color{blue}{+3x} & = &-17 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+6} \\\Leftrightarrow & 8x+3x& = &-17+6 \\\Leftrightarrow & 11x& = &-11 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-11}{ \color{red}{11} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x-5)& = & 15 \color{red}{+} (6-5x) \\\Leftrightarrow & -36x-30& = &15+6-5x \\\Leftrightarrow & -36x \color{red}{-30} & = &21 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-30} \color{blue}{+30} \color{blue}{+5x} & = &21 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+30} \\\Leftrightarrow & -36x+5x& = &21+30 \\\Leftrightarrow & -31x& = &51 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{51}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-51}{31} & & \\ & V = \left\{ \frac{-51}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-x+6)& = & -9 \color{red}{-} (-10-3x) \\\Leftrightarrow & -4x+24& = &-9+10+3x \\\Leftrightarrow & -4x \color{red}{+24} & = &1 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+24} \color{blue}{-24} \color{blue}{-3x} & = &1 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-24} \\\Leftrightarrow & -4x-3x& = &1-24 \\\Leftrightarrow & -7x& = &-23 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-23}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{23}{7} & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (2x-2)& = & 7 \color{red}{-} (-3+x) \\\Leftrightarrow & 8x-8& = &7+3-x \\\Leftrightarrow & 8x \color{red}{-8} & = &10 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{-8} \color{blue}{+8} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+8} \\\Leftrightarrow & 8x+x& = &10+8 \\\Leftrightarrow & 9x& = &18 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{18}{ \color{red}{9} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-2x-7)& = & 9 \color{red}{-} (2-5x) \\\Leftrightarrow & -6x-21& = &9-2+5x \\\Leftrightarrow & -6x \color{red}{-21} & = &7 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-21} \color{blue}{+21} \color{blue}{-5x} & = &7 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+21} \\\Leftrightarrow & -6x-5x& = &7+21 \\\Leftrightarrow & -11x& = &28 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{28}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-28}{11} & & \\ & V = \left\{ \frac{-28}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x-3)& = & -11 \color{red}{-} (5-3x) \\\Leftrightarrow & 10x-6& = &-11-5+3x \\\Leftrightarrow & 10x \color{red}{-6} & = &-16 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{-6} \color{blue}{+6} \color{blue}{-3x} & = &-16 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+6} \\\Leftrightarrow & 10x-3x& = &-16+6 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-3x-2)& = & 9 \color{red}{-} (-6+4x) \\\Leftrightarrow & -9x-6& = &9+6-4x \\\Leftrightarrow & -9x \color{red}{-6} & = &15 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-6} \color{blue}{+6} \color{blue}{+4x} & = &15 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+6} \\\Leftrightarrow & -9x+4x& = &15+6 \\\Leftrightarrow & -5x& = &21 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{21}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{-21}{5} & & \\ & V = \left\{ \frac{-21}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{4} (-5x+2)& = & -11 \color{red}{-} (-2+x) \\\Leftrightarrow & -20x+8& = &-11+2-x \\\Leftrightarrow & -20x \color{red}{+8} & = &-9 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -20x+x& = &-9-8 \\\Leftrightarrow & -19x& = &-17 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{-17}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{17}{19} & & \\ & V = \left\{ \frac{17}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-6x-1)& = & 3 \color{red}{-} (10+x) \\\Leftrightarrow & -12x-2& = &3-10-x \\\Leftrightarrow & -12x \color{red}{-2} & = &-7 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-2} \color{blue}{+2} \color{blue}{+x} & = &-7 \color{red}{-x} \color{blue}{+x} \color{blue}{+2} \\\Leftrightarrow & -12x+x& = &-7+2 \\\Leftrightarrow & -11x& = &-5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{5}{11} & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)