Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (-2x-5)& = & 2 \color{red}{+} (-5-5x) \\\Leftrightarrow & -6x-15& = &2-5-5x \\\Leftrightarrow & -6x \color{red}{-15} & = &-3 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-15} \color{blue}{+15} \color{blue}{+5x} & = &-3 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+15} \\\Leftrightarrow & -6x+5x& = &-3+15 \\\Leftrightarrow & -x& = &12 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{12}{ \color{red}{-1} } \\\Leftrightarrow & x = -12 & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-2x+5)& = & 11 \color{red}{-} (3+3x) \\\Leftrightarrow & -4x+10& = &11-3-3x \\\Leftrightarrow & -4x \color{red}{+10} & = &8 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{+10} \color{blue}{-10} \color{blue}{+3x} & = &8 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-10} \\\Leftrightarrow & -4x+3x& = &8-10 \\\Leftrightarrow & -x& = &-2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-2}{ \color{red}{-1} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (5x+6)& = & 5 \color{red}{-} (13-3x) \\\Leftrightarrow & 25x+30& = &5-13+3x \\\Leftrightarrow & 25x \color{red}{+30} & = &-8 \color{red}{+3x} \\\Leftrightarrow & 25x \color{red}{+30} \color{blue}{-30} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-30} \\\Leftrightarrow & 25x-3x& = &-8-30 \\\Leftrightarrow & 22x& = &-38 \\\Leftrightarrow & \frac{22x}{ \color{red}{22} }& = &\frac{-38}{ \color{red}{22} } \\\Leftrightarrow & x = \frac{-19}{11} & & \\ & V = \left\{ \frac{-19}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (4x-7)& = & 1 \color{red}{+} (3+x) \\\Leftrightarrow & 12x-21& = &1+3+x \\\Leftrightarrow & 12x \color{red}{-21} & = &4 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-21} \color{blue}{+21} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+21} \\\Leftrightarrow & 12x-x& = &4+21 \\\Leftrightarrow & 11x& = &25 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{25}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{25}{11} & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (5x+6)& = & 13 \color{red}{-} (-7+x) \\\Leftrightarrow & 30x+36& = &13+7-x \\\Leftrightarrow & 30x \color{red}{+36} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & 30x+x& = &20-36 \\\Leftrightarrow & 31x& = &-16 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{-16}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{-16}{31} & & \\ & V = \left\{ \frac{-16}{31} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+6)& = & -13 \color{red}{+} (11+x) \\\Leftrightarrow & 24x+36& = &-13+11+x \\\Leftrightarrow & 24x \color{red}{+36} & = &-2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+36} \color{blue}{-36} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{-36} \\\Leftrightarrow & 24x-x& = &-2-36 \\\Leftrightarrow & 23x& = &-38 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-38}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-38}{23} & & \\ & V = \left\{ \frac{-38}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{3} (-6x-6)& = & 2 \color{red}{-} (12+x) \\\Leftrightarrow & -18x-18& = &2-12-x \\\Leftrightarrow & -18x \color{red}{-18} & = &-10 \color{red}{-x} \\\Leftrightarrow & -18x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-10 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & -18x+x& = &-10+18 \\\Leftrightarrow & -17x& = &8 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{8}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-8}{17} & & \\ & V = \left\{ \frac{-8}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (-2x-3)& = & -2 \color{red}{+} (6+x) \\\Leftrightarrow & -8x-12& = &-2+6+x \\\Leftrightarrow & -8x \color{red}{-12} & = &4 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &4 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -8x-x& = &4+12 \\\Leftrightarrow & -9x& = &16 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{16}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-16}{9} & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{6} (5x-1)& = & 9 \color{red}{-} (-11+x) \\\Leftrightarrow & 30x-6& = &9+11-x \\\Leftrightarrow & 30x \color{red}{-6} & = &20 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & 30x+x& = &20+6 \\\Leftrightarrow & 31x& = &26 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{26}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{26}{31} & & \\ & V = \left\{ \frac{26}{31} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (x-4)& = & 1 \color{red}{+} (-3-5x) \\\Leftrightarrow & 3x-12& = &1-3-5x \\\Leftrightarrow & 3x \color{red}{-12} & = &-2 \color{red}{-5x} \\\Leftrightarrow & 3x \color{red}{-12} \color{blue}{+12} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+12} \\\Leftrightarrow & 3x+5x& = &-2+12 \\\Leftrightarrow & 8x& = &10 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = &\frac{10}{ \color{red}{8} } \\\Leftrightarrow & x = \frac{5}{4} & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (-2x+7)& = & -3 \color{red}{-} (-15+x) \\\Leftrightarrow & -12x+42& = &-3+15-x \\\Leftrightarrow & -12x \color{red}{+42} & = &12 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{+42} \color{blue}{-42} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-42} \\\Leftrightarrow & -12x+x& = &12-42 \\\Leftrightarrow & -11x& = &-30 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-30}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{30}{11} & & \\ & V = \left\{ \frac{30}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (x-5)& = & -13 \color{red}{+} (-9+x) \\\Leftrightarrow & 2x-10& = &-13-9+x \\\Leftrightarrow & 2x \color{red}{-10} & = &-22 \color{red}{+x} \\\Leftrightarrow & 2x \color{red}{-10} \color{blue}{+10} \color{blue}{-x} & = &-22 \color{red}{+x} \color{blue}{-x} \color{blue}{+10} \\\Leftrightarrow & 2x-x& = &-22+10 \\\Leftrightarrow & x& = &-12 \\ & V = \left\{ -12 \right\} & \\\end{align}\)