Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (5x+7)& = & 9 \color{red}{-} (-15+x) \\\Leftrightarrow & 10x+14& = &9+15-x \\\Leftrightarrow & 10x \color{red}{+14} & = &24 \color{red}{-x} \\\Leftrightarrow & 10x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &24 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & 10x+x& = &24-14 \\\Leftrightarrow & 11x& = &10 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{10}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (3x-4)& = & 5 \color{red}{+} (14-5x) \\\Leftrightarrow & 18x-24& = &5+14-5x \\\Leftrightarrow & 18x \color{red}{-24} & = &19 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &19 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & 18x+5x& = &19+24 \\\Leftrightarrow & 23x& = &43 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{43}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{43}{23} & & \\ & V = \left\{ \frac{43}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-3x+2)& = & 9 \color{red}{-} (-1+x) \\\Leftrightarrow & -12x+8& = &9+1-x \\\Leftrightarrow & -12x \color{red}{+8} & = &10 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+8} \color{blue}{-8} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-8} \\\Leftrightarrow & -12x+x& = &10-8 \\\Leftrightarrow & -11x& = &2 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{2}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-6x+6)& = & -7 \color{red}{+} (13-5x) \\\Leftrightarrow & -36x+36& = &-7+13-5x \\\Leftrightarrow & -36x \color{red}{+36} & = &6 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{+36} \color{blue}{-36} \color{blue}{+5x} & = &6 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-36} \\\Leftrightarrow & -36x+5x& = &6-36 \\\Leftrightarrow & -31x& = &-30 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-30}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{30}{31} & & \\ & V = \left\{ \frac{30}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-6)& = & 10 \color{red}{+} (-5+x) \\\Leftrightarrow & -12x-18& = &10-5+x \\\Leftrightarrow & -12x \color{red}{-18} & = &5 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -12x-x& = &5+18 \\\Leftrightarrow & -13x& = &23 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{23}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-23}{13} & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-2x-7)& = & -1 \color{red}{-} (8+x) \\\Leftrightarrow & -12x-42& = &-1-8-x \\\Leftrightarrow & -12x \color{red}{-42} & = &-9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & -12x+x& = &-9+42 \\\Leftrightarrow & -11x& = &33 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{33}{ \color{red}{-11} } \\\Leftrightarrow & x = -3 & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x-6)& = & -2 \color{red}{+} (11+x) \\\Leftrightarrow & 18x-18& = &-2+11+x \\\Leftrightarrow & 18x \color{red}{-18} & = &9 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & 18x-x& = &9+18 \\\Leftrightarrow & 17x& = &27 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{27}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{27}{17} & & \\ & V = \left\{ \frac{27}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-5x-5)& = & 12 \color{red}{+} (15+3x) \\\Leftrightarrow & -20x-20& = &12+15+3x \\\Leftrightarrow & -20x \color{red}{-20} & = &27 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &27 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & -20x-3x& = &27+20 \\\Leftrightarrow & -23x& = &47 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{47}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-47}{23} & & \\ & V = \left\{ \frac{-47}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (3x-3)& = & -4 \color{red}{-} (-14+x) \\\Leftrightarrow & 9x-9& = &-4+14-x \\\Leftrightarrow & 9x \color{red}{-9} & = &10 \color{red}{-x} \\\Leftrightarrow & 9x \color{red}{-9} \color{blue}{+9} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{+9} \\\Leftrightarrow & 9x+x& = &10+9 \\\Leftrightarrow & 10x& = &19 \\\Leftrightarrow & \frac{10x}{ \color{red}{10} }& = &\frac{19}{ \color{red}{10} } \\\Leftrightarrow & x = \frac{19}{10} & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (5x+2)& = & -14 \color{red}{+} (7-2x) \\\Leftrightarrow & 15x+6& = &-14+7-2x \\\Leftrightarrow & 15x \color{red}{+6} & = &-7 \color{red}{-2x} \\\Leftrightarrow & 15x \color{red}{+6} \color{blue}{-6} \color{blue}{+2x} & = &-7 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-6} \\\Leftrightarrow & 15x+2x& = &-7-6 \\\Leftrightarrow & 17x& = &-13 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-13}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-13}{17} & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x+5)& = & 5 \color{red}{+} (2-5x) \\\Leftrightarrow & 6x+30& = &5+2-5x \\\Leftrightarrow & 6x \color{red}{+30} & = &7 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{+5x} & = &7 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-30} \\\Leftrightarrow & 6x+5x& = &7-30 \\\Leftrightarrow & 11x& = &-23 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-23}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-23}{11} & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-7)& = & 12 \color{red}{-} (-8+x) \\\Leftrightarrow & -4x-14& = &12+8-x \\\Leftrightarrow & -4x \color{red}{-14} & = &20 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-14} \color{blue}{+14} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+14} \\\Leftrightarrow & -4x+x& = &20+14 \\\Leftrightarrow & -3x& = &34 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{34}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{-34}{3} & & \\ & V = \left\{ \frac{-34}{3} \right\} & \\\end{align}\)