Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (5x+4)& = & 6 \color{red}{+} (-5-3x) \\\Leftrightarrow & 25x+20& = &6-5-3x \\\Leftrightarrow & 25x \color{red}{+20} & = &1 \color{red}{-3x} \\\Leftrightarrow & 25x \color{red}{+20} \color{blue}{-20} \color{blue}{+3x} & = &1 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-20} \\\Leftrightarrow & 25x+3x& = &1-20 \\\Leftrightarrow & 28x& = &-19 \\\Leftrightarrow & \frac{28x}{ \color{red}{28} }& = &\frac{-19}{ \color{red}{28} } \\\Leftrightarrow & x = \frac{-19}{28} & & \\ & V = \left\{ \frac{-19}{28} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-4x+7)& = & -8 \color{red}{+} (-15-5x) \\\Leftrightarrow & -16x+28& = &-8-15-5x \\\Leftrightarrow & -16x \color{red}{+28} & = &-23 \color{red}{-5x} \\\Leftrightarrow & -16x \color{red}{+28} \color{blue}{-28} \color{blue}{+5x} & = &-23 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-28} \\\Leftrightarrow & -16x+5x& = &-23-28 \\\Leftrightarrow & -11x& = &-51 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-51}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{51}{11} & & \\ & V = \left\{ \frac{51}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{6} (-5x+4)& = & 10 \color{red}{+} (-15+x) \\\Leftrightarrow & -30x+24& = &10-15+x \\\Leftrightarrow & -30x \color{red}{+24} & = &-5 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & -30x-x& = &-5-24 \\\Leftrightarrow & -31x& = &-29 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-29}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{29}{31} & & \\ & V = \left\{ \frac{29}{31} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{6} (-x-2)& = & 7 \color{red}{-} (-7-5x) \\\Leftrightarrow & -6x-12& = &7+7+5x \\\Leftrightarrow & -6x \color{red}{-12} & = &14 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-12} \color{blue}{+12} \color{blue}{-5x} & = &14 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+12} \\\Leftrightarrow & -6x-5x& = &14+12 \\\Leftrightarrow & -11x& = &26 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{26}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-26}{11} & & \\ & V = \left\{ \frac{-26}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{5} (-5x-6)& = & 14 \color{red}{+} (4+x) \\\Leftrightarrow & -25x-30& = &14+4+x \\\Leftrightarrow & -25x \color{red}{-30} & = &18 \color{red}{+x} \\\Leftrightarrow & -25x \color{red}{-30} \color{blue}{+30} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{+30} \\\Leftrightarrow & -25x-x& = &18+30 \\\Leftrightarrow & -26x& = &48 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = &\frac{48}{ \color{red}{-26} } \\\Leftrightarrow & x = \frac{-24}{13} & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (3x-4)& = & -10 \color{red}{-} (-7-5x) \\\Leftrightarrow & 18x-24& = &-10+7+5x \\\Leftrightarrow & 18x \color{red}{-24} & = &-3 \color{red}{+5x} \\\Leftrightarrow & 18x \color{red}{-24} \color{blue}{+24} \color{blue}{-5x} & = &-3 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+24} \\\Leftrightarrow & 18x-5x& = &-3+24 \\\Leftrightarrow & 13x& = &21 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{21}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{21}{13} & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-4x-7)& = & -5 \color{red}{+} (11+x) \\\Leftrightarrow & -24x-42& = &-5+11+x \\\Leftrightarrow & -24x \color{red}{-42} & = &6 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-42} \color{blue}{+42} \color{blue}{-x} & = &6 \color{red}{+x} \color{blue}{-x} \color{blue}{+42} \\\Leftrightarrow & -24x-x& = &6+42 \\\Leftrightarrow & -25x& = &48 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{48}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-48}{25} & & \\ & V = \left\{ \frac{-48}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (2x-2)& = & -4 \color{red}{-} (11-3x) \\\Leftrightarrow & 4x-4& = &-4-11+3x \\\Leftrightarrow & 4x \color{red}{-4} & = &-15 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-4} \color{blue}{+4} \color{blue}{-3x} & = &-15 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+4} \\\Leftrightarrow & 4x-3x& = &-15+4 \\\Leftrightarrow & x& = &-11 \\ & V = \left\{ -11 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{5} (-2x-3)& = & -3 \color{red}{-} (-5+3x) \\\Leftrightarrow & -10x-15& = &-3+5-3x \\\Leftrightarrow & -10x \color{red}{-15} & = &2 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & -10x+3x& = &2+15 \\\Leftrightarrow & -7x& = &17 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{17}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-17}{7} & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-6x-3)& = & 9 \color{red}{+} (10+x) \\\Leftrightarrow & -30x-15& = &9+10+x \\\Leftrightarrow & -30x \color{red}{-15} & = &19 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{-15} \color{blue}{+15} \color{blue}{-x} & = &19 \color{red}{+x} \color{blue}{-x} \color{blue}{+15} \\\Leftrightarrow & -30x-x& = &19+15 \\\Leftrightarrow & -31x& = &34 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{34}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-34}{31} & & \\ & V = \left\{ \frac{-34}{31} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (6x-7)& = & -4 \color{red}{-} (-12+x) \\\Leftrightarrow & 36x-42& = &-4+12-x \\\Leftrightarrow & 36x \color{red}{-42} & = &8 \color{red}{-x} \\\Leftrightarrow & 36x \color{red}{-42} \color{blue}{+42} \color{blue}{+x} & = &8 \color{red}{-x} \color{blue}{+x} \color{blue}{+42} \\\Leftrightarrow & 36x+x& = &8+42 \\\Leftrightarrow & 37x& = &50 \\\Leftrightarrow & \frac{37x}{ \color{red}{37} }& = &\frac{50}{ \color{red}{37} } \\\Leftrightarrow & x = \frac{50}{37} & & \\ & V = \left\{ \frac{50}{37} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{3} (4x-6)& = & 5 \color{red}{-} (9+x) \\\Leftrightarrow & 12x-18& = &5-9-x \\\Leftrightarrow & 12x \color{red}{-18} & = &-4 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{-18} \color{blue}{+18} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+18} \\\Leftrightarrow & 12x+x& = &-4+18 \\\Leftrightarrow & 13x& = &14 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{14}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{14}{13} & & \\ & V = \left\{ \frac{14}{13} \right\} & \\\end{align}\)