Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-6x-1)& = & -5 \color{red}{+} (6-5x) \\\Leftrightarrow & -36x-6& = &-5+6-5x \\\Leftrightarrow & -36x \color{red}{-6} & = &1 \color{red}{-5x} \\\Leftrightarrow & -36x \color{red}{-6} \color{blue}{+6} \color{blue}{+5x} & = &1 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+6} \\\Leftrightarrow & -36x+5x& = &1+6 \\\Leftrightarrow & -31x& = &7 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{7}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-7}{31} & & \\ & V = \left\{ \frac{-7}{31} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{6} (-6x+4)& = & -2 \color{red}{-} (-8+x) \\\Leftrightarrow & -36x+24& = &-2+8-x \\\Leftrightarrow & -36x \color{red}{+24} & = &6 \color{red}{-x} \\\Leftrightarrow & -36x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & -36x+x& = &6-24 \\\Leftrightarrow & -35x& = &-18 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = &\frac{-18}{ \color{red}{-35} } \\\Leftrightarrow & x = \frac{18}{35} & & \\ & V = \left\{ \frac{18}{35} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (3x+4)& = & 11 \color{red}{-} (10+x) \\\Leftrightarrow & 12x+16& = &11-10-x \\\Leftrightarrow & 12x \color{red}{+16} & = &1 \color{red}{-x} \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-16} \\\Leftrightarrow & 12x+x& = &1-16 \\\Leftrightarrow & 13x& = &-15 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-15}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-15}{13} & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (-6x+3)& = & 12 \color{red}{+} (13+x) \\\Leftrightarrow & -30x+15& = &12+13+x \\\Leftrightarrow & -30x \color{red}{+15} & = &25 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+15} \color{blue}{-15} \color{blue}{-x} & = &25 \color{red}{+x} \color{blue}{-x} \color{blue}{-15} \\\Leftrightarrow & -30x-x& = &25-15 \\\Leftrightarrow & -31x& = &10 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{10}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{-10}{31} & & \\ & V = \left\{ \frac{-10}{31} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{4} (-3x-6)& = & 7 \color{red}{+} (-9+x) \\\Leftrightarrow & -12x-24& = &7-9+x \\\Leftrightarrow & -12x \color{red}{-24} & = &-2 \color{red}{+x} \\\Leftrightarrow & -12x \color{red}{-24} \color{blue}{+24} \color{blue}{-x} & = &-2 \color{red}{+x} \color{blue}{-x} \color{blue}{+24} \\\Leftrightarrow & -12x-x& = &-2+24 \\\Leftrightarrow & -13x& = &22 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{22}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-22}{13} & & \\ & V = \left\{ \frac{-22}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (-3x+4)& = & -6 \color{red}{+} (10-2x) \\\Leftrightarrow & -15x+20& = &-6+10-2x \\\Leftrightarrow & -15x \color{red}{+20} & = &4 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+20} \color{blue}{-20} \color{blue}{+2x} & = &4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-20} \\\Leftrightarrow & -15x+2x& = &4-20 \\\Leftrightarrow & -13x& = &-16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{16}{13} & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (-5x+6)& = & 3 \color{red}{-} (-7+x) \\\Leftrightarrow & -30x+36& = &3+7-x \\\Leftrightarrow & -30x \color{red}{+36} & = &10 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{+36} \color{blue}{-36} \color{blue}{+x} & = &10 \color{red}{-x} \color{blue}{+x} \color{blue}{-36} \\\Leftrightarrow & -30x+x& = &10-36 \\\Leftrightarrow & -29x& = &-26 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{-26}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{26}{29} & & \\ & V = \left\{ \frac{26}{29} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{4} (3x+6)& = & 7 \color{red}{+} (4+x) \\\Leftrightarrow & 12x+24& = &7+4+x \\\Leftrightarrow & 12x \color{red}{+24} & = &11 \color{red}{+x} \\\Leftrightarrow & 12x \color{red}{+24} \color{blue}{-24} \color{blue}{-x} & = &11 \color{red}{+x} \color{blue}{-x} \color{blue}{-24} \\\Leftrightarrow & 12x-x& = &11-24 \\\Leftrightarrow & 11x& = &-13 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-13}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-13}{11} & & \\ & V = \left\{ \frac{-13}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (2x+2)& = & -5 \color{red}{+} (10-5x) \\\Leftrightarrow & 6x+6& = &-5+10-5x \\\Leftrightarrow & 6x \color{red}{+6} & = &5 \color{red}{-5x} \\\Leftrightarrow & 6x \color{red}{+6} \color{blue}{-6} \color{blue}{+5x} & = &5 \color{red}{-5x} \color{blue}{+5x} \color{blue}{-6} \\\Leftrightarrow & 6x+5x& = &5-6 \\\Leftrightarrow & 11x& = &-1 \\\Leftrightarrow & \frac{11x}{ \color{red}{11} }& = &\frac{-1}{ \color{red}{11} } \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-2x-3)& = & -10 \color{red}{-} (-14+3x) \\\Leftrightarrow & -10x-15& = &-10+14-3x \\\Leftrightarrow & -10x \color{red}{-15} & = &4 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{-15} \color{blue}{+15} \color{blue}{+3x} & = &4 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+15} \\\Leftrightarrow & -10x+3x& = &4+15 \\\Leftrightarrow & -7x& = &19 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{19}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-19}{7} & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-4x+2)& = & 11 \color{red}{+} (7+x) \\\Leftrightarrow & -8x+4& = &11+7+x \\\Leftrightarrow & -8x \color{red}{+4} & = &18 \color{red}{+x} \\\Leftrightarrow & -8x \color{red}{+4} \color{blue}{-4} \color{blue}{-x} & = &18 \color{red}{+x} \color{blue}{-x} \color{blue}{-4} \\\Leftrightarrow & -8x-x& = &18-4 \\\Leftrightarrow & -9x& = &14 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = &\frac{14}{ \color{red}{-9} } \\\Leftrightarrow & x = \frac{-14}{9} & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{2} (-x+3)& = & 4 \color{red}{-} (8+x) \\\Leftrightarrow & -2x+6& = &4-8-x \\\Leftrightarrow & -2x \color{red}{+6} & = &-4 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+6} \color{blue}{-6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{-6} \\\Leftrightarrow & -2x+x& = &-4-6 \\\Leftrightarrow & -x& = &-10 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-10}{ \color{red}{-1} } \\\Leftrightarrow & x = 10 & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)