Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x-4)& = & 4 \color{red}{+} (-15+x) \\\Leftrightarrow & -36x-24& = &4-15+x \\\Leftrightarrow & -36x \color{red}{-24} & = &-11 \color{red}{+x} \\\Leftrightarrow & -36x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -36x-x& = &-11+24 \\\Leftrightarrow & -37x& = &13 \\\Leftrightarrow & \frac{-37x}{ \color{red}{-37} }& = &\frac{13}{ \color{red}{-37} } \\\Leftrightarrow & x = \frac{-13}{37} & & \\ & V = \left\{ \frac{-13}{37} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-x-2)& = & -4 \color{red}{-} (-4+3x) \\\Leftrightarrow & -4x-8& = &-4+4-3x \\\Leftrightarrow & -4x \color{red}{-8} & = &0 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-8} \color{blue}{+8} \color{blue}{+3x} & = &0 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+8} \\\Leftrightarrow & -4x+3x& = &0+8 \\\Leftrightarrow & -x& = &8 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{8}{ \color{red}{-1} } \\\Leftrightarrow & x = -8 & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (3x-6)& = & -13 \color{red}{-} (-14+x) \\\Leftrightarrow & 6x-12& = &-13+14-x \\\Leftrightarrow & 6x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 6x+x& = &1+12 \\\Leftrightarrow & 7x& = &13 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{13}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{13}{7} & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (6x+1)& = & -2 \color{red}{+} (1+x) \\\Leftrightarrow & 30x+5& = &-2+1+x \\\Leftrightarrow & 30x \color{red}{+5} & = &-1 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-1 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & 30x-x& = &-1-5 \\\Leftrightarrow & 29x& = &-6 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-6}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-6}{29} & & \\ & V = \left\{ \frac{-6}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-2)& = & 8 \color{red}{-} (7+x) \\\Leftrightarrow & -12x-6& = &8-7-x \\\Leftrightarrow & -12x \color{red}{-6} & = &1 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -12x+x& = &1+6 \\\Leftrightarrow & -11x& = &7 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{7}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-7}{11} & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (6x-5)& = & -6 \color{red}{+} (10+x) \\\Leftrightarrow & 12x-10& = &-6+10+x \\\Leftrightarrow & 12x \color{red}{-10} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 12x-x& = &4+10 \\\Leftrightarrow & 11x& = &14 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{14}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-4x-6)& = & 6 \color{red}{+} (14+3x) \\\Leftrightarrow & -8x-12& = &6+14+3x \\\Leftrightarrow & -8x \color{red}{-12} & = &20 \color{red}{+3x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-3x} & = &20 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+12} \\\Leftrightarrow & -8x-3x& = &20+12 \\\Leftrightarrow & -11x& = &32 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{32}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-32}{11} & & \\ & V = \left\{ \frac{-32}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-5x+3)& = & -9 \color{red}{-} (7+x) \\\Leftrightarrow & -15x+9& = &-9-7-x \\\Leftrightarrow & -15x \color{red}{+9} & = &-16 \color{red}{-x} \\\Leftrightarrow & -15x \color{red}{+9} \color{blue}{-9} \color{blue}{+x} & = &-16 \color{red}{-x} \color{blue}{+x} \color{blue}{-9} \\\Leftrightarrow & -15x+x& = &-16-9 \\\Leftrightarrow & -14x& = &-25 \\\Leftrightarrow & \frac{-14x}{ \color{red}{-14} }& = &\frac{-25}{ \color{red}{-14} } \\\Leftrightarrow & x = \frac{25}{14} & & \\ & V = \left\{ \frac{25}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (5x+7)& = & 14 \color{red}{-} (-9-2x) \\\Leftrightarrow & 15x+21& = &14+9+2x \\\Leftrightarrow & 15x \color{red}{+21} & = &23 \color{red}{+2x} \\\Leftrightarrow & 15x \color{red}{+21} \color{blue}{-21} \color{blue}{-2x} & = &23 \color{red}{+2x} \color{blue}{-2x} \color{blue}{-21} \\\Leftrightarrow & 15x-2x& = &23-21 \\\Leftrightarrow & 13x& = &2 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{2}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{2}{13} & & \\ & V = \left\{ \frac{2}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (4x+7)& = & 1 \color{red}{+} (-13-5x) \\\Leftrightarrow & 8x+14& = &1-13-5x \\\Leftrightarrow & 8x \color{red}{+14} & = &-12 \color{red}{-5x} \\\Leftrightarrow & 8x \color{red}{+14} \color{blue}{-14} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-14} \\\Leftrightarrow & 8x+5x& = &-12-14 \\\Leftrightarrow & 13x& = &-26 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-26}{ \color{red}{13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (3x-5)& = & -11 \color{red}{+} (6+x) \\\Leftrightarrow & 9x-15& = &-11+6+x \\\Leftrightarrow & 9x \color{red}{-15} & = &-5 \color{red}{+x} \\\Leftrightarrow & 9x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & 9x-x& = &-5+15 \\\Leftrightarrow & 8x& = &10 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{10}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{5}{4} & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x-4)& = & -3 \color{red}{+} (-4+3x) \\\Leftrightarrow & 25x-20& = &-3-4+3x \\\Leftrightarrow & 25x \color{red}{-20} & = &-7 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{-20} \color{blue}{+20} \color{blue}{-3x} & = &-7 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+20} \\\Leftrightarrow & 25x-3x& = &-7+20 \\\Leftrightarrow & 22x& = &13 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{13}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{13}{22} & & \\ & V = \left\{ \frac{13}{22} \right\} & \\\end{align}\)