Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{2} (-5x+1)& = & 8 \color{red}{-} (-1+x) \\\Leftrightarrow & -10x+2& = &8+1-x \\\Leftrightarrow & -10x \color{red}{+2} & = &9 \color{red}{-x} \\\Leftrightarrow & -10x \color{red}{+2} \color{blue}{-2} \color{blue}{+x} & = &9 \color{red}{-x} \color{blue}{+x} \color{blue}{-2} \\\Leftrightarrow & -10x+x& = &9-2 \\\Leftrightarrow & -9x& = &7 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{7}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-7}{9} & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-4x+1)& = & -6 \color{red}{+} (-8+x) \\\Leftrightarrow & -20x+5& = &-6-8+x \\\Leftrightarrow & -20x \color{red}{+5} & = &-14 \color{red}{+x} \\\Leftrightarrow & -20x \color{red}{+5} \color{blue}{-5} \color{blue}{-x} & = &-14 \color{red}{+x} \color{blue}{-x} \color{blue}{-5} \\\Leftrightarrow & -20x-x& = &-14-5 \\\Leftrightarrow & -21x& = &-19 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = &\frac{-19}{ \color{red}{-21} } \\\Leftrightarrow & x = \frac{19}{21} & & \\ & V = \left\{ \frac{19}{21} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{3} (6x+7)& = & -4 \color{red}{+} (11+x) \\\Leftrightarrow & 18x+21& = &-4+11+x \\\Leftrightarrow & 18x \color{red}{+21} & = &7 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{+21} \color{blue}{-21} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-21} \\\Leftrightarrow & 18x-x& = &7-21 \\\Leftrightarrow & 17x& = &-14 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{-14}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{-14}{17} & & \\ & V = \left\{ \frac{-14}{17} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x-7)& = & 15 \color{red}{+} (15+x) \\\Leftrightarrow & 18x-21& = &15+15+x \\\Leftrightarrow & 18x \color{red}{-21} & = &30 \color{red}{+x} \\\Leftrightarrow & 18x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &30 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 18x-x& = &30+21 \\\Leftrightarrow & 17x& = &51 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{51}{ \color{red}{17} } \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (x-5)& = & -9 \color{red}{-} (-7+x) \\\Leftrightarrow & 2x-10& = &-9+7-x \\\Leftrightarrow & 2x \color{red}{-10} & = &-2 \color{red}{-x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+10} \\\Leftrightarrow & 2x+x& = &-2+10 \\\Leftrightarrow & 3x& = &8 \\\Leftrightarrow & \frac{3x}{ \color{red}{3} }& = &\frac{8}{ \color{red}{3} } \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (4x+3)& = & -12 \color{red}{+} (2+x) \\\Leftrightarrow & 20x+15& = &-12+2+x \\\Leftrightarrow & 20x \color{red}{+15} & = &-10 \color{red}{+x} \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &-10 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & 20x-x& = &-10-15 \\\Leftrightarrow & 19x& = &-25 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-25}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{-25}{19} & & \\ & V = \left\{ \frac{-25}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (6x+5)& = & -9 \color{red}{+} (-9+x) \\\Leftrightarrow & 36x+30& = &-9-9+x \\\Leftrightarrow & 36x \color{red}{+30} & = &-18 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 36x-x& = &-18-30 \\\Leftrightarrow & 35x& = &-48 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-48}{ \color{red}{35} } \\\Leftrightarrow & x = \frac{-48}{35} & & \\ & V = \left\{ \frac{-48}{35} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-2x+1)& = & 1 \color{red}{-} (-13+x) \\\Leftrightarrow & -12x+6& = &1+13-x \\\Leftrightarrow & -12x \color{red}{+6} & = &14 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -12x+x& = &14-6 \\\Leftrightarrow & -11x& = &8 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{8}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (4x-6)& = & 6 \color{red}{-} (-9+x) \\\Leftrightarrow & 24x-36& = &6+9-x \\\Leftrightarrow & 24x \color{red}{-36} & = &15 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-36} \color{blue}{+36} \color{blue}{+x} & = &15 \color{red}{-x} \color{blue}{+x} \color{blue}{+36} \\\Leftrightarrow & 24x+x& = &15+36 \\\Leftrightarrow & 25x& = &51 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{51}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{51}{25} & & \\ & V = \left\{ \frac{51}{25} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x-5)& = & 1 \color{red}{-} (-12-3x) \\\Leftrightarrow & -10x-25& = &1+12+3x \\\Leftrightarrow & -10x \color{red}{-25} & = &13 \color{red}{+3x} \\\Leftrightarrow & -10x \color{red}{-25} \color{blue}{+25} \color{blue}{-3x} & = &13 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+25} \\\Leftrightarrow & -10x-3x& = &13+25 \\\Leftrightarrow & -13x& = &38 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{38}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-38}{13} & & \\ & V = \left\{ \frac{-38}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (4x-5)& = & -4 \color{red}{-} (9+x) \\\Leftrightarrow & 24x-30& = &-4-9-x \\\Leftrightarrow & 24x \color{red}{-30} & = &-13 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &-13 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & 24x+x& = &-13+30 \\\Leftrightarrow & 25x& = &17 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{17}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{17}{25} & & \\ & V = \left\{ \frac{17}{25} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (2x+3)& = & -7 \color{red}{+} (14+x) \\\Leftrightarrow & 6x+9& = &-7+14+x \\\Leftrightarrow & 6x \color{red}{+9} & = &7 \color{red}{+x} \\\Leftrightarrow & 6x \color{red}{+9} \color{blue}{-9} \color{blue}{-x} & = &7 \color{red}{+x} \color{blue}{-x} \color{blue}{-9} \\\Leftrightarrow & 6x-x& = &7-9 \\\Leftrightarrow & 5x& = &-2 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{-2}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)