Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-6x-6)& = & -11 \color{red}{+} (6+x) \\\Leftrightarrow & -18x-18& = &-11+6+x \\\Leftrightarrow & -18x \color{red}{-18} & = &-5 \color{red}{+x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+18} \\\Leftrightarrow & -18x-x& = &-5+18 \\\Leftrightarrow & -19x& = &13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{13}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-13}{19} & & \\ & V = \left\{ \frac{-13}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-4x-1)& = & 2 \color{red}{+} (3+x) \\\Leftrightarrow & -8x-2& = &2+3+x \\\Leftrightarrow & -8x \color{red}{-2} & = &5 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-2} \color{blue}{+2} \color{blue}{-x} & = &5 \color{red}{+x} \color{blue}{-x} \color{blue}{+2} \\\Leftrightarrow & -8x-x& = &5+2 \\\Leftrightarrow & -9x& = &7 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{7}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-7}{9} & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x+2)& = & 6 \color{red}{+} (-11+x) \\\Leftrightarrow & -30x+12& = &6-11+x \\\Leftrightarrow & -30x \color{red}{+12} & = &-5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-12} \\\Leftrightarrow & -30x-x& = &-5-12 \\\Leftrightarrow & -31x& = &-17 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-17}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{17}{31} & & \\ & V = \left\{ \frac{17}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x+1)& = & -4 \color{red}{-} (2-5x) \\\Leftrightarrow & 6x+3& = &-4-2+5x \\\Leftrightarrow & 6x \color{red}{+3} & = &-6 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{+3} \color{blue}{-3} \color{blue}{-5x} & = &-6 \color{red}{+5x} \color{blue}{-5x} \color{blue}{-3} \\\Leftrightarrow & 6x-5x& = &-6-3 \\\Leftrightarrow & x& = &-9 \\ & V = \left\{ -9 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-6x+7)& = & -12 \color{red}{-} (-12+x) \\\Leftrightarrow & -36x+42& = &-12+12-x \\\Leftrightarrow & -36x \color{red}{+42} & = &0 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &0 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -36x+x& = &0-42 \\\Leftrightarrow & -35x& = &-42 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-42}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-6x+3)& = & -12 \color{red}{-} (7+x) \\\Leftrightarrow & -24x+12& = &-12-7-x \\\Leftrightarrow & -24x \color{red}{+12} & = &-19 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+12} \color{blue}{-12} \color{blue}{+x} & = &-19 \color{red}{-x} \color{blue}{+x} \color{blue}{-12} \\\Leftrightarrow & -24x+x& = &-19-12 \\\Leftrightarrow & -23x& = &-31 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-31}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{31}{23} & & \\ & V = \left\{ \frac{31}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (6x+5)& = & -14 \color{red}{-} (9+x) \\\Leftrightarrow & 18x+15& = &-14-9-x \\\Leftrightarrow & 18x \color{red}{+15} & = &-23 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+15} \color{blue}{-15} \color{blue}{+x} & = &-23 \color{red}{-x} \color{blue}{+x} \color{blue}{-15} \\\Leftrightarrow & 18x+x& = &-23-15 \\\Leftrightarrow & 19x& = &-38 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{-38}{ \color{red}{19} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{3} (x-7)& = & 8 \color{red}{-} (12-2x) \\\Leftrightarrow & 3x-21& = &8-12+2x \\\Leftrightarrow & 3x \color{red}{-21} & = &-4 \color{red}{+2x} \\\Leftrightarrow & 3x \color{red}{-21} \color{blue}{+21} \color{blue}{-2x} & = &-4 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+21} \\\Leftrightarrow & 3x-2x& = &-4+21 \\\Leftrightarrow & x& = &17 \\ & V = \left\{ 17 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (2x-6)& = & 9 \color{red}{+} (14+x) \\\Leftrightarrow & 12x-36& = &9+14+x \\\Leftrightarrow & 12x \color{red}{-36} & = &23 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-36} \color{blue}{+36} \color{blue}{-x} & = &23 \color{red}{+x} \color{blue}{-x} \color{blue}{+36} \\\Leftrightarrow & 12x-x& = &23+36 \\\Leftrightarrow & 11x& = &59 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{59}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{59}{11} & & \\ & V = \left\{ \frac{59}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (-x-6)& = & 3 \color{red}{-} (9+x) \\\Leftrightarrow & -3x-18& = &3-9-x \\\Leftrightarrow & -3x \color{red}{-18} & = &-6 \color{red}{-x} \\\Leftrightarrow & -3x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -3x+x& = &-6+18 \\\Leftrightarrow & -2x& = &12 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = &\frac{12}{ \color{red}{-2} } \\\Leftrightarrow & x = -6 & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (5x+5)& = & -5 \color{red}{+} (7-3x) \\\Leftrightarrow & 10x+10& = &-5+7-3x \\\Leftrightarrow & 10x \color{red}{+10} & = &2 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & 10x+3x& = &2-10 \\\Leftrightarrow & 13x& = &-8 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-8}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (5x+6)& = & -14 \color{red}{-} (-11+2x) \\\Leftrightarrow & 25x+30& = &-14+11-2x \\\Leftrightarrow & 25x \color{red}{+30} & = &-3 \color{red}{-2x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{+2x} & = &-3 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-30} \\\Leftrightarrow & 25x+2x& = &-3-30 \\\Leftrightarrow & 27x& = &-33 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = &\frac{-33}{ \color{red}{27} } \\\Leftrightarrow & x = \frac{-11}{9} & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)