Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (x-5)& = & -1 \color{red}{-} (-5-5x) \\\Leftrightarrow & 6x-30& = &-1+5+5x \\\Leftrightarrow & 6x \color{red}{-30} & = &4 \color{red}{+5x} \\\Leftrightarrow & 6x \color{red}{-30} \color{blue}{+30} \color{blue}{-5x} & = &4 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+30} \\\Leftrightarrow & 6x-5x& = &4+30 \\\Leftrightarrow & x& = &34 \\ & V = \left\{ 34 \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{2} (-5x-3)& = & -5 \color{red}{+} (-15+x) \\\Leftrightarrow & -10x-6& = &-5-15+x \\\Leftrightarrow & -10x \color{red}{-6} & = &-20 \color{red}{+x} \\\Leftrightarrow & -10x \color{red}{-6} \color{blue}{+6} \color{blue}{-x} & = &-20 \color{red}{+x} \color{blue}{-x} \color{blue}{+6} \\\Leftrightarrow & -10x-x& = &-20+6 \\\Leftrightarrow & -11x& = &-14 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-14}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{14}{11} & & \\ & V = \left\{ \frac{14}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-2x+6)& = & 10 \color{red}{-} (-1-3x) \\\Leftrightarrow & -4x+12& = &10+1+3x \\\Leftrightarrow & -4x \color{red}{+12} & = &11 \color{red}{+3x} \\\Leftrightarrow & -4x \color{red}{+12} \color{blue}{-12} \color{blue}{-3x} & = &11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-12} \\\Leftrightarrow & -4x-3x& = &11-12 \\\Leftrightarrow & -7x& = &-1 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-1}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (6x+1)& = & 9 \color{red}{-} (-13+x) \\\Leftrightarrow & 18x+3& = &9+13-x \\\Leftrightarrow & 18x \color{red}{+3} & = &22 \color{red}{-x} \\\Leftrightarrow & 18x \color{red}{+3} \color{blue}{-3} \color{blue}{+x} & = &22 \color{red}{-x} \color{blue}{+x} \color{blue}{-3} \\\Leftrightarrow & 18x+x& = &22-3 \\\Leftrightarrow & 19x& = &19 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{19}{ \color{red}{19} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-2x-4)& = & 3 \color{red}{-} (-9-5x) \\\Leftrightarrow & -8x-16& = &3+9+5x \\\Leftrightarrow & -8x \color{red}{-16} & = &12 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-16} \color{blue}{+16} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+16} \\\Leftrightarrow & -8x-5x& = &12+16 \\\Leftrightarrow & -13x& = &28 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{28}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-28}{13} & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{4} (-3x-3)& = & 3 \color{red}{+} (11+x) \\\Leftrightarrow & -12x-12& = &3+11+x \\\Leftrightarrow & -12x \color{red}{-12} & = &14 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &14 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -12x-x& = &14+12 \\\Leftrightarrow & -13x& = &26 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{26}{ \color{red}{-13} } \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x+4)& = & 10 \color{red}{+} (-15+x) \\\Leftrightarrow & -30x+24& = &10-15+x \\\Leftrightarrow & -30x \color{red}{+24} & = &-5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -30x-x& = &-5-24 \\\Leftrightarrow & -31x& = &-29 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-29}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{29}{31} & & \\ & V = \left\{ \frac{29}{31} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (5x-3)& = & 11 \color{red}{-} (8+x) \\\Leftrightarrow & 30x-18& = &11-8-x \\\Leftrightarrow & 30x \color{red}{-18} & = &3 \color{red}{-x} \\\Leftrightarrow & 30x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &3 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 30x+x& = &3+18 \\\Leftrightarrow & 31x& = &21 \\\Leftrightarrow & \frac{31x}{ \color{red}{31} }& = &\frac{21}{ \color{red}{31} } \\\Leftrightarrow & x = \frac{21}{31} & & \\ & V = \left\{ \frac{21}{31} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (5x+4)& = & 4 \color{red}{-} (15-3x) \\\Leftrightarrow & 10x+8& = &4-15+3x \\\Leftrightarrow & 10x \color{red}{+8} & = &-11 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-11 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & 10x-3x& = &-11-8 \\\Leftrightarrow & 7x& = &-19 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-19}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{3} (4x-4)& = & 10 \color{red}{+} (-1+x) \\\Leftrightarrow & 12x-12& = &10-1+x \\\Leftrightarrow & 12x \color{red}{-12} & = &9 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &9 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & 12x-x& = &9+12 \\\Leftrightarrow & 11x& = &21 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{21}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{21}{11} & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{3} (-x+7)& = & -3 \color{red}{+} (-9-5x) \\\Leftrightarrow & -3x+21& = &-3-9-5x \\\Leftrightarrow & -3x \color{red}{+21} & = &-12 \color{red}{-5x} \\\Leftrightarrow & -3x \color{red}{+21} \color{blue}{-21} \color{blue}{+5x} & = &-12 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-21} \\\Leftrightarrow & -3x+5x& = &-12-21 \\\Leftrightarrow & 2x& = &-33 \\\Leftrightarrow & \frac{2x}{ \color{red}{2} }& = &\frac{-33}{ \color{red}{2} } \\\Leftrightarrow & x = \frac{-33}{2} & & \\ & V = \left\{ \frac{-33}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (-3x-5)& = & 10 \color{red}{+} (-5-4x) \\\Leftrightarrow & -9x-15& = &10-5-4x \\\Leftrightarrow & -9x \color{red}{-15} & = &5 \color{red}{-4x} \\\Leftrightarrow & -9x \color{red}{-15} \color{blue}{+15} \color{blue}{+4x} & = &5 \color{red}{-4x} \color{blue}{+4x} \color{blue}{+15} \\\Leftrightarrow & -9x+4x& = &5+15 \\\Leftrightarrow & -5x& = &20 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{20}{ \color{red}{-5} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)