Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (-3x-3)& = & -9 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x-12& = &-9-2+x \\\Leftrightarrow & -12x \color{red}{-12} & = &-11 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-11 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &-11+12 \\\Leftrightarrow & -13x& = &1 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{1}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-1}{13} & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (2x-5)& = & 11 \color{red}{-} (-2+x) \\\Leftrightarrow & 4x-10& = &11+2-x \\\Leftrightarrow & 4x \color{red}{-10} & = &13 \color{red}{-x} \\\Leftrightarrow & 4x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 4x+x& = &13+10 \\\Leftrightarrow & 5x& = &23 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{23}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{23}{5} & & \\ & V = \left\{ \frac{23}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (-2x-2)& = & 11 \color{red}{+} (-9+3x) \\\Leftrightarrow & -10x-10& = &11-9+3x \\\Leftrightarrow & -10x \color{red}{-10} & = &2 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-10} \color{blue}{+10} \color{blue}{-3x} & = &2 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+10} \\\Leftrightarrow & -10x-3x& = &2+10 \\\Leftrightarrow & -13x& = &12 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{12}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-12}{13} & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x+7)& = & -10 \color{red}{+} (8-5x) \\\Leftrightarrow & 18x+21& = &-10+8-5x \\\Leftrightarrow & 18x \color{red}{+21} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 18x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & 18x+5x& = &-2-21 \\\Leftrightarrow & 23x& = &-23 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-23}{ \color{red}{23} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (x+5)& = & 8 \color{red}{+} (8+x) \\\Leftrightarrow & 6x+30& = &8+8+x \\\Leftrightarrow & 6x \color{red}{+30} & = &16 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &16 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 6x-x& = &16-30 \\\Leftrightarrow & 5x& = &-14 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-14}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-14}{5} & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (x+1)& = & -2 \color{red}{+} (5-5x) \\\Leftrightarrow & 6x+6& = &-2+5-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &3 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &3-6 \\\Leftrightarrow & 11x& = &-3 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-3}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (-5x-6)& = & -10 \color{red}{-} (-11+x) \\\Leftrightarrow & -10x-12& = &-10+11-x \\\Leftrightarrow & -10x \color{red}{-12} & = &1 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -10x+x& = &1+12 \\\Leftrightarrow & -9x& = &13 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{13}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-13}{9} & & \\ & V = \left\{ \frac{-13}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (-x-6)& = & 1 \color{red}{+} (1+2x) \\\Leftrightarrow & -3x-18& = &1+1+2x \\\Leftrightarrow & -3x \color{red}{-18} & = &2 \color{red}{+2x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{-2x} & = &2 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+18} \\\Leftrightarrow & -3x-2x& = &2+18 \\\Leftrightarrow & -5x& = &20 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{20}{ \color{red}{-5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (6x+2)& = & -5 \color{red}{-} (-12+x) \\\Leftrightarrow & 36x+12& = &-5+12-x \\\Leftrightarrow & 36x \color{red}{+12} & = &7 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & 36x+x& = &7-12 \\\Leftrightarrow & 37x& = &-5 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{-5}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{-5}{37} & & \\ & V = \left\{ \frac{-5}{37} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (5x-2)& = & -8 \color{red}{+} (1+x) \\\Leftrightarrow & 25x-10& = &-8+1+x \\\Leftrightarrow & 25x \color{red}{-10} & = &-7 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-7 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 25x-x& = &-7+10 \\\Leftrightarrow & 24x& = &3 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{3}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x-1)& = & -13 \color{red}{+} (-2+x) \\\Leftrightarrow & -12x-6& = &-13-2+x \\\Leftrightarrow & -12x \color{red}{-6} & = &-15 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-15 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -12x-x& = &-15+6 \\\Leftrightarrow & -13x& = &-9 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-9}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{9}{13} & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-2x-6)& = & -7 \color{red}{-} (6+x) \\\Leftrightarrow & -4x-12& = &-7-6-x \\\Leftrightarrow & -4x \color{red}{-12} & = &-13 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -4x+x& = &-13+12 \\\Leftrightarrow & -3x& = &-1 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{-1}{ \color{red}{-3} } \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)